CBSE Questions for Class 11 Commerce Applied Mathematics Functions Quiz 7 - MCQExams.com

Let f : $$R \to R$$ and g : $$R \to R$$ be two one-one and onto functions such that they are the mirror images of each other about the line y =If h(x) = f(x) + g(x), then h(0) equal to
  • 2
  • 4
  • 0
  • 1
$$c \to c\,\,is\,defined\,as\,f\left( x \right) = \frac{{ax + b}}{{cx + d}}\,\,bd \ne 0$$.then f is a constant function when
  • a=c
  • b=d
  • ad=bc
  • ab=cd
Let $$A$$ be a set of $$4$$ elements and $$B$$ has $$3$$ elements . From the set of all functions from $$A$$ to $$B$$, the probability that it is an onto function is
  • $$\dfrac{4}{9}$$
  • $$0$$
  • $$\dfrac{29}{32}$$
  • $$1$$
If $$f : A \rightarrow B $$ defined as $$f(x) = x^2+2x+\frac{1}{1+(x+1)^2}$$ is onto function, then set B is equal to
  • $$[0, \infty)$$
  • $$(-\infty, 0)$$
  • $$[2, \infty)$$
  • $$(-\infty, \infty)$$
Find the domain on which the function $$f(x) = 2x^2 -5$$ and $$g(x) = 5x - 2$$ are equal.
  • $$3,-\dfrac{1}{2}$$
  • $$-3,-\dfrac{1}{2}$$
  • $$3,\dfrac{1}{2}$$
  • $$-3,\dfrac{1}{2}$$
The domain of the function $$f(x) = \dfrac{1}{\log_{10}(1-x)} + \sqrt{x+2}$$ is equal to 
  • $$[-3, -2.5) \cup (-2.5, 2]$$
  • $$[-2, 0) \cup (0, 1]$$
  • $$[0,1]$$
  • None of these
If $$g(f(x) ) = |\sin x |$$ and $$f(g(x))=(\sin\sqrt x)^2$$ , then 
  • $$f(x) = \sin^2x. g(x) =\sqrt x$$
  • $$f(x) = \sin x , g(x) =|x| $$
  • $$f(x) = x^2, g(x) = \sin \sqrt x$$
  • f and g can not be determined
Let $$f$$, $$g:R\rightarrow {R}$$ be two functions defined as $$ f\left( x \right) =\left| x \right| +x$$, $$ g\left( x \right) =\left| x \right| -x, \forall x\in R$$. Then, find $$fog(x)$$ 
  • $$||x|-x|-|x|-x$$
  • $$||x|-x|+|x|-x$$
  • $$||x|-x|-|x|+x$$
  • None of thesse
The set of all values of $$x$$ for which $$ \dfrac { \sqrt { -{ x }^{ 2 }+5x-6 }  }{ \sqrt { 1-2\left\{ x \right\}  }  } \ge 0$$ is (where{.} denotes the fractional part function)
  • $$\left[2,\dfrac{5}{2}\right]\cup{3}$$
  • $$(2, 3)$$
  • $$\left[\dfrac{5}{2},\ 3\right]$$
  • $$\left[2,\dfrac{5}{2}\right]\cup\left[\dfrac{5}{2}, 3\right]$$
Consider set $$A={1,2,3,4}$$ and set $$B={0,2,4,6,8}$$, then the number of one-one function from set $$A$$ to set $$B$$ is ?
  • $$5$$
  • $$24$$
  • $$120$$
  • None of these
The set onto which the derivative of the function $$f(x)=x(\log x-1)$$ maps the range $$[1,\infty )$$ is
  • $$\left[1,\infty \right)$$
  • $$\left( e,\infty \right)$$
  • $$\left[e,\infty \right)$$
  • $$\left( 0,0 \right)$$
If $$f(x)=2x+5$$ and $$g(x)=x^2+1$$ be two real function , then value of $$fog$$ at x=1
  • $$9$$
  • $$6$$
  • $$5$$
  • $$4$$
If $$f ( x ) = \left( a - x ^ { n } \right) ^ { 1 / n }$$ where $$a > 0$$ and $$n$$ is a positive integer then $$( f o f ) ( x )$$ is 
  • $$f ( x )$$
  • $$x$$
  • $$0$$
  • $$1$$
The domain of the function, $$f(x) = \dfrac{\sqrt{\sin x}}{\sqrt{(x - 2)(8 - x)}}$$ is
  • $$[0, \pi] \cup [2\pi, 8)$$
  • $$(2, \pi] \cup [2\pi, 8)$$
  • $$(2, 8)$$
  • $$(0, 8)$$
Let $$E=\{1, 2, 3, 4\}$$ and $$F=\{1, 2\}$$ then the number of onto functions from E to F is
  • $$14$$
  • $$16$$
  • $$12$$
  • $$8$$
Let $$f\left( x \right) ={ x }^{ 2 },g\left( x \right) ={ 2 }^{ x }$$, then solution set of $$fog\left( x \right) =gof\left( x \right) $$ is
  • R
  • $$\left\{ 0 \right\} $$
  • $$\left\{ 0,2 \right\} $$
  • None of these
Let $$f(x+\dfrac{1}{x})=x^2+\dfrac{1}{x^2}(x\neq 0)$$, then $$f(x)=$$
  • $$x^2$$
  • $$x^2-1$$
  • $$x^2-2$$
  • N.O.T
If a relation $$'R'$$ is defined by $$R = \left\{ {\left( {x,y} \right)/2{x^2} + 3{y^2} \le 6} \right\},$$ then the domain of $$R(x,y)$$ is 
  • $$x\in \left[ { - 3,3} \right]$$
  • $$x\in \left[ { - \sqrt 3 ,\sqrt 3 } \right]$$
  • $$y\in \left[ { - \sqrt 2 ,\sqrt 2 } \right]$$
  • $$y\in \left[ { - 2,2} \right]$$
If $$f\left( x \right) =\begin{cases} 2+x,\quad x\ge 0 \\ 2-x,\quad x<0 \end{cases}$$ then $$f\left( f\left( x \right)  \right) $$ is given by
  • $$f\left( f\left( x \right) \right) =\begin{cases} 2+x,\quad x\ge 0 \\ 4-x,\quad x<0 \end{cases}$$
  • $$f\left( f\left( x \right) \right) =\begin{cases} 2+x,\quad x\ge 0 \\ 2-x,\quad x<0 \end{cases}$$
  • $$f\left( f\left( x \right) \right) =\begin{cases} 4+x,\quad x< 0 \\ x,\quad x\ge 0 \end{cases}$$
  • $$f\left( f\left( x \right) \right) =\begin{cases} 4+x,\quad x\ge 0 \\ x,\quad x<0 \end{cases}$$
If $$(x)$$ is defined on $$(0,1)$$ then the domain of defination of $$f[({e^x})]$$ $$+f\left( {ln\,\left| x \right|} \right)$$ is subset of
  • $$(-e,-1)$$
  • $$(-e,-1) (1,e)$$
  • $$( - \infty , - 1)(1,\infty )$$
  • $$(-e,e)$$
If f(x)=sin log $$\left( {\sqrt {4 - {x^2}} /\left( {1 - x} \right)} \right)$$ then the domain and range f are (respectively)
  • $$[-1,1],(-1,1)$$
  • $$(-2,1),(-1,1)$$
  • $$(1,2),[-1,1]$$
  • $$(-2,1),[-1,1]$$
If f(g(x))=5x+2 and g(x)=8x then f(x)=
  • $$ \frac{5}{8}x+2$$.
  • $$ \frac{8}{5}x+2$$.
  • $$ \frac{5}{8}x-2$$.
  • 8x-2
  • 5x-2
Let $$g\left( x \right) =1+x-\left[ x \right] $$ and $$f\left( x \right) =\begin{cases} -1,x<0 \\ 0,x=0 \\ 1,x>0 \end{cases}$$ Then for all $$x,f\left( g\left( x \right) \right) $$ is equal to (where $$\left[ . \right] $$ represents the greatest integer function)
  • $$x$$
  • $$1$$
  • $$f\left( x \right)$$
  • $$g\left( x \right)$$
If : $$f(x) = 5 {x}^{2}$$, $$g(x) = 3x^{4}$$, then : $$(fog) (-1) =$$ 
  • $$45$$
  • $$-54$$
  • $$-32$$
  • $$-64$$
Let $$f:X \to \left[ {1,\,27} \right]$$ be  a function by $$f\left( x \right) = 5\sin x + 12\cos x + 14$$. The set $$X$$ so that $$f$$ is one-one and onto is 
  • $$\left[ { - \pi /2,\pi /2\,} \right]$$
  • $$\left[ {0,\,\pi } \right]$$
  • $$\left[ {0,\,\pi /2} \right]$$
  • non of these
The distinct linear functions which maps from $$[-1,1]$$ onto $$[0,2]$$ are 
  • $$x+1$$, $$-x+1$$
  • $$x-1$$, $$x+1$$
  • $$-x+1$$
  • $$-x+2$$
For $$a,\ b\ \in \ R-\left\{ 0 \right\}$$, let $$f(x)=ax^{2}+bx+a$$ satisfies $$f\left(x+\dfrac{7}{4}\right)=f\left(\dfrac{7}{4}-x\right) \forall \ x\ \in\ R$$.
Also the equation $$f(x)=7x+a$$ has only one real distinct solution. The minimum value of $$f(x)$$ in $$\left[0,\dfrac{3}{2}\right]$$ is equal to
  • $$\dfrac{-33}{8}$$
  • $$0$$
  • $$4$$
  • $$-2$$
If $$ f ( x ) = \left( a - x ^ { n } \right) ^ { 1 / n }$$ where $$ a > 0$$ and } $$n$$ is a positive integer then$$( f o f ) ( x )$$ is
  • $$f ( x )$$
  • x
  • 0
  • 1
The identity function on real numbers given by $$f(x)=x$$ is continuous at every real numbers.
  • True
  • False
The set of all $$x$$ for which the functions are not defined
$$f\left( x \right) =\log _{ [(x-2)/( x+3)]}2 $$ and $$g\left( x \right) =\dfrac { 1 }{ \sqrt { { x }^{ 2 }-9 }  } $$, is
  • $$\left[ -3,2 \right] $$
  • $$\left[ -3,2 \right) $$
  • $$(-3,2]$$
  • $$\left( -3,-2 \right) $$
If $$f:R \rightarrow R, f(x)=2x-1$$ and $$g; R \rightarrow R, g(x)=x^{2}+2$$, then $$(gof)(x)$$ equals-
  • $$2x^{2}-1$$
  • $$(2x-1)^{2}$$
  • $$2x^{2}+3$$
  • $$4x^{2}-4x+3$$
The domain of definition of
$$f\left( x \right) =\sqrt { \log _{ 0.4 }{ \frac { x-1 }{ x+5 }  }  } \times \dfrac { 1 }{ { x }^{ 2 }-36 } $$, is
  • $$\left( -\infty ,0 \right) -\left\{ -6 \right\} $$
  • $$\left( 0,\infty \right) -\left\{ 1,6 \right\} $$
  • $$\left( 1,\infty \right) -\left\{ 6 \right\} $$
  • $$\left( 1,\infty \right) +\left\{ 6 \right\} $$
If $$f\left( x \right) = (1 - x)$$ , $$x \in \left[ { - 3,3} \right]$$ , then the domain of $$f\left( {f\left( x \right)} \right)$$ is
  • $$\left[ { - 2,3} \right]$$
  • $$\left( { - 2,3} \right)$$
  • $$\left[ { - 2,3]} \right.$$
  • $$( - 2,3]$$
If $$\log_2\left ( 3^{2x+2}+7 \right )=2+\log_2\left ( 3^{x-1}+1 \right )$$, then number of real values of $$x$$ is/are
  • $$0$$
  • $$1$$
  • $$2$$
  • $$4$$
If $$f(x)=\frac{x}{\sqrt{1-x^{2}}}$$ and g(x) = $$f(x)=\frac{x}{\sqrt{1+x^{2}}}$$ , then (fog)(x) =
  • $$f(x)=\frac{x}{\sqrt{1-x^{2}}}$$
  • $$f(x)=\frac{x}{\sqrt{1+x^{2}}}$$
  • $$x^{2}$$
  • x
The domain of the function $$f\left( x \right) = \sqrt {x - \sqrt {1 - {x^2}} } $$ is
  • $$\left[ { - 1, - \dfrac{1}{{\sqrt 2 }}} \right] \cup \left[ {\dfrac{1}{{\sqrt 2 }},1} \right]$$
  • $$\left[ { - 1,1} \right]$$
  • $$( - \infty , - \dfrac{1}{2}] \cup [\dfrac{1}{{\sqrt 2 }},\infty )$$
  • $$\left[ {\dfrac{1}{{\sqrt 2 }},1} \right]$$
The domain of the functions $$f(x)=\sqrt { \log { \left( 2x-{ x }^{ 2 } \right)  }  } $$ is
  • $$(0,2)$$
  • $$[0,2]$$
  • $$\left\{ 1 \right\} $$
  • none
The domain of the function $$f(x)=\cfrac { 1 }{ \sqrt { \left| x \right| -x }  } $$ is
  • $$(-\infty, \infty)$$
  • $$(0,\infty)$$
  • $$(-\infty, 0)$$
  • $$(-\infty, \infty)-\left\{ 0 \right\} $$
Let $$g(x)=1+x-[x]\quad $$ and $$f(x)=\begin{cases} -1\quad if\quad x<0 \\ 0\quad \quad if\quad x=0 \\ 1\quad \quad if\quad x>0 \end{cases}$$ , then $$\forall \:x,fog(x)$$ equals 
  • $$x$$
  • $$1$$
  • $$f(x)$$
  • $$g(x)$$
$$f:c \to c$$ is defined as $$f(x) = \dfrac{{ax + b}}{{cx + d}},bd \ne 0$$ then $$f$$ is a constant function when,
  • a=c
  • b=d
  • ad=bc
  • ab=cd
Let f(x)= max { 1+sinx, 1, 1 -cosx}, $$x \epsilon [0, 2 \pi]$$ and g(x)= max {1, |x-1|} $$x \epsilon R$$, then
  • g(f(0))=1
  • g(f(1))=1
  • f(f(1))=1
  • f(g(0))=1+sin1
If $$f(x)=\frac{1}{x},g(x)=\frac{1}{x^{2}} $$ and h $$(x)= x^{2},$$ then
  • $$fog (x)= x^{2}, x\neq \bar{0}, h(g(x))= \frac{1}{x^{2}}$$
  • $$h(g(x))= \frac{1}{x^{2}}x\neq 0, fog(x)= x^{2}$$
  • $$fog(x)=x^{2},x\neq 0,h(g(x))= (g(x))^{2},x\neq 0$$
  • None of these
if $$f\left( x \right) = \log \left( {\dfrac{{1 +x}}{{1 - x}}} \right)$$ and $$g\left( x \right) = \dfrac{{3x + {x^3}}}{{1 + 3{x^2}}}$$ then $$\left( {f(g(x)))} \right)$$ is equal to
  • $$ - f\left( x \right)$$
  • $$3f\left( x \right)$$
  • $${\left( {f\left( x \right)} \right)^3}$$
  • $$f\left( {3x} \right)$$
Let $$f:R\rightarrow R$$ is a function satisfying $$f(2-x)=f(2+x)$$ and $$f(20-x)=f(x)\forall x\in R$$
If $$f(0)=5$$ then the minimum possible no. of values of $$x$$ satisfying $$f(x)=5$$ for $$x=[0.,70]$$, is
  • $$21$$
  • $$12$$
  • $$11$$
  • $$22$$
Let $$f\left( x \right) = {x^2}$$ and $$g\left( x \right) = {2^x}$$. Then the solution of the equation $$fog\left( x \right) = gof\left( x \right)$$ is
  • $$R$$
  • $$\left\{ {0} \right\}$$
  • $$\left\{ {0,\,2} \right\}$$
  • none
All values of a for which f : R $$ \to R$$ defined by f(x)= $${x^3} + a{x^2} + 3x + 100$$ is a one one functions, are
  • $$( - \infty , - 2)$$
  • $$( - \infty ,4)$$
  • $$(4, - 4)$$
  • $$( - 3,3)$$
Domain of $$f\left( x \right) = \sin ^{ -1 }{ \left[ \log _{ 2 }{ \left( \frac { { x }^{ 2 } }{ 2 }  \right)  }  \right]  } $$, where $$\left[ . \right] $$ denotes greatest integer functions, is
  • $$\left[ -\sqrt { 8, } \sqrt { 8 } \right] $$
  • $$\left[ -\sqrt { 8, } -1 \right] \cup (1,\quad \sqrt { 8 } ]$$
  • $$(-2,-1)\cup (1,2)$$
  • None of these
If $$f(x)$$ is defined on $$(0,1)$$  then the domain of definition of $$f({e}^{x})+f(\ln{\left| x \right| })$$ is
  • $$(-e,-1)$$
  • $$(-e,-1)\cup (1,e)$$
  • $$(-5,-1)\cup (1,\infty)$$
  • $$(-e,e)$$
The domain of $$\sqrt {|x - 2| - 1}  + \sqrt {3 - |x - 2|} \,\,is\,$$
  • $$[ - 1,3]\, \cup \,[5,\infty )$$
  • $$[ - 1,5]$$
  • $$[1,3]$$
  • $$[ - 1,1] \cup [3,5]$$
$$f:R \rightarrow R$$ such that $$f(x)=\ell n(x+\sqrt {x^{2}+1})$$. Another function $$g(x)$$ is defined such that $$gof(x)=x\ \forall\ x \in\ R$$. Then $$g(2)$$ is -
  • $$\dfrac {e^{2}+e^{-2}}{2}$$
  • $$e^{2}$$
  • $$\dfrac {e^{2}-e^{-2}}{2}$$
  • $$e^{-2}$$
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