CBSE Questions for Class 11 Commerce Applied Mathematics Functions Quiz 13 - MCQExams.com

Let f(x)= $$y=\begin{cases} { x }^{ 2 }-3x+4\quad \quad :\quad X<3 \\ \quad \quad \quad x+7\quad \quad :\quad X\ge 3 \end{cases}\quad and\quad g(x)=\begin{cases} \quad \quad x+6\quad \quad \quad :\quad X<4 \\ { x }^{ 2 }+x+2\quad \quad :\quad X\ge 4 \end{cases}$$
then which of the following is/ are true-
  • $$(f+g) (1)=9$$
  • $$(f-g)(3.5)= 1$$
  • $$(f+g) (0)=24$$
  • $$\left( \dfrac { f }{ g } \right) (5)=\dfrac { 8 }{ 3 } $$
If =$$f=\left\{ (-2,4),(0,6),(2,8) \right\} $$ and 
$$g=\left\{ (-2,-1),(0,3),(2,5) \right\} $$, then 
$$\left( \frac { 2f }{ 3g } +\frac { 3g }{ 2f }  \right) (0)=\quad $$
  • 1/12
  • 25/12
  • 5/12
  • 13/12
If f(x)=x+tanx and g(x) is inverse of f(x) then g'(x) is equal to 
  • $$\dfrac { 1 }{ 1+(g(x)-{ x) }^{ 2 } } $$
  • $$\dfrac { 1 }{ 1-(g(x)-{ x) }^{ 2 } } $$
  • $$\dfrac { 1 }{ 1+(g(x)-{ x) }^{ 2 } } $$
  • $$\dfrac { 1 }{ 2-(g(x)-{ x) }^{ 2 } } $$
Number of solution of the equation  $$f ( x ) = g ( x )$$  are same as number of point of intersection of the curves $$y = f ( x )$$  and  $$y = g ( x )$$  hence answer the following question.
Number of the solution of the equation  $$x ^ { 2 } = | x - 2 | + | x + 2 | - 1$$  is
  • $$0$$
  • $$3$$
  • $$2$$
  • $$4$$
For the function $$F(x)=\sqrt { { 4-x }^{ 2 } } +\sqrt { { x }^{ 2 }-1 } $$
  • Domain is (-2,2)
  • Domain is (-2, -1) (1,2)
  • Range is $$\left( \sqrt { 3 } ,\sqrt { 5 } \right) $$
  • Range is $$\left( \sqrt { 3 } ,\sqrt { 6 } \right) $$
If f(x) = x + 4, g(x) = 5x and h(x) = 12/x. find the value of $$f^{ -1 }$$ (g(h(6))).
  • 10
  • 14
  • 6
  • 0
Let $$f(x)=x+\cos x+2$$ and g(x) be the  inverse function of f(x) then $$g^1(3)=$$
  • $$1$$
  • $$2$$
  • $$3$$
  • $$0$$
If $$f:A\rightarrow B$$ given by $${ 3 }^{ f(x) }+{ 2 }^{ -x }=4$$ is a bijection, then
  • $$A=\left\{ x\in R:-1< x< \infty \right\} ;B=\left\{ x\in R:2< x< 4 \right\} $$
  • $$A=\left\{ x\in R:-3< x <\infty \right\} ;B=\left\{ x\in R:0 < x <4 \right\} $$
  • $$A=\left\{ x\in R:-2< x <\infty \right\} ;B=\left\{ x\in R:0< x <4 \right\} $$
  • None of these
If $$f(x)=8x^3$$ and $$g(x)=x^{1/3}$$ then $$(g o f)(x)=?$$
  • $$x$$
  • $$2x$$
  • $$\dfrac{x}{2}$$
  • $$3x^2$$
If $$f(x)=\dfrac{1}{(1-x)}$$ then $$(f o f o f)(x)=?$$
  • $$\dfrac{1}{(1-3x)}$$
  • $$\dfrac{x}{(1+3x)}$$
  • $$x$$
  • None of these
If $$f(x)=x^2, g(x)=\tan x$$ and $$h(x)=log x$$ then $$\{h o (g o f)\}\left(\sqrt{\dfrac{\pi}{4}}\right)=?$$
  • $$0$$
  • $$1$$
  • $$\dfrac{1}{x}$$
  • $$\dfrac{1}{2} \log \dfrac{\pi}{4}$$
If $$f=\{(1, 2), (3, 5), (4, 1)\}$$ and $$g=\{(2, 3), (5, 1), (1, 3)\}$$ then $$(g o f)=?$$
  • $$\{(3, 1), (1, 3), (3, 4)\}$$
  • $$\{(1, 3), (3, 1), (4, 3)\}$$
  • $$\{(3, 4), (4, 3), (1, 3)\}$$
  • $$\{(2, 5), (5, 2), (1, 5)\}$$
If $$f(x)=(x^2-1)$$ and $$g(x)=(2x+3)$$ then $$(g o f)(x)=?$$
  • $$(2x^2+3)$$
  • $$(3x^2+2)$$
  • $$(2x^2+1)$$
  • None of these
If $$f(x)=x^2-3x+2$$ then $$(f o f)(x)=?$$
  • $$x^4$$
  • $$x^4-6x^3$$
  • $$x^4-6x^3+10x^2$$
  • None of these
Which of the following is not true about $$h_2(x)$$
  • Domain R
  • It periodic function with period $$2\pi$$
  • Range is [0, 1]
  • None of these
Let $$f: R \rightarrow R$$ defined by $$f(x)= e\frac { { e }^{ { x }^{ 2 } }-{ e }^{ { -x }^{ 2 } } }{ { e }^{ { x }^{ 2 } }+{ e }^{ { -x }^{ 2 } } } $$ then 
  • $$f(x)$$ is one-one but not onto
  • $$f(x)$$ is neither one-one nor onto
  • $$f(x)$$ is many one but onto
  • $$f(x)$$ is one-one and onto
If $$ f(x)=\dfrac{2}{x-3}, g(x)=\dfrac{x-3}{x+4} $$ and $$ h(x)=-\dfrac{2(2 x+1)}{x^{2}+x-12} $$ then $$ \lim _{x \rightarrow 3}[f(x)+g(x)+h(x)] $$ is
  • $$ -2 $$
  • $$ -1 $$
  • $$ -\dfrac{2}{7} $$
  • 0
Which of thefollowing functions are indentical?
  • f(x)= ln $$x^{2}$$ and g(x)= 2 In x
  • f(x)= $$log_x e$$ and $$g(x)= \dfrac{1}{log_e x}$$
  • f(x)= sin $$(cos^{-1}x)$$ and g(x)= $$cos({sin^{-1}x})$$
  • none of these
For  a real number y, let [y] denotes the greatest integer less than or equal to y. Then the function
$$ f(x)= \dfrac{tan(\pi \left[ x-\pi  \right ])}{1+[x]^2} $$ is
  • discontinuous at some x
  • continuous at all x, but the derivative $$ f'(x_{0}) $$ does not exist for some x
  • $$ f'(x) $$ exist for all x but the derivative $$ f'(x_{0}) $$ does not exist second for some x
  • $$ f'(x) $$ exists for all x
The domain of the function $$f(x) = \sqrt{\ln_{(|x| - 1)} \left (x^{2} + 4x +4 \right )} $$ is 
  • $$\left [ -3, -1 \right ] \cup \left [1, 2 \right ]$$
  • $$\left ( -3, -1 \right ) \cup \left [2, \infty \right )$$
  • $$\left ( -\infty, -3 \right ] \cup \left (-2, -1 \right ) \cup \left (2, \infty \right )$$
  • None of these
The number of roots of the equation g(x) = 1 is
  • 2
  • 1
  • 3
  • 0
If $$f : X \rightarrow Y$$, where  $$X$$ and $$Y$$ are sets containing natural numbers, $$f(x) = \frac{x + 5} {x + 2}$$ then the number of elements in the domain and range of $$f(x) are respectively
  • 1 and 1
  • 2 and 1
  • 2 and 2
  • 1 and 2
The domain of the $$f(x) = \frac{1} {\sqrt{4x - |x^{2} -10x + 9|}}$$ is
  • $$\left (7 - \sqrt{40}, 7 + \sqrt{40} \right )$$
  • $$\left (0, 7 + \sqrt{40} \right )$$
  • $$\left (7 - \sqrt{40}, \infty \right )$$
  • None of these
If A  = { 1 ,2 , 3 , 4} , then which following is a function in A
  • $$ f_{1} = {(x , y) : y = x + 1} $$
  • $$ f_{2} = {( x , y) : x + y > 4 } $$
  • $$ f_{3} = {( x , y) : y < x} $$
  • $$ f_{4} = { ( x , y) : x + y = 5} $$
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