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JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

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Application +4 | -1

Let

f:(-1,1) \rightarrow R

defined by

f(x)=\ln \left(\frac{1+x}{1-x}\right)

and

g: R \rightarrow(-1,1)

defined by

g(x)=\frac{3 x+x^3}{1+3 x^2}

, then

f(g(x))

is equal to:

View answer and explanation

Correct option: C

3 f(x)

Option C (

3 f(x)

) is correct because substituting

g(x)

into

f(x)

and simplifying the logarithm results in

3f(x)

.

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

f(x)=x(4-x)

f^{-1}(x)

is given by: If

g(f(x))=|\sin x|

f(g(x))=(\sin \sqrt{x})^2

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

f\left( x \right) = x - \left[ x \right]

{f^{ - 1}}\left( x \right)

f: R \rightarrow R

f(x)=x^4

, Choose the correct answer. Which of the following functions are odd functions Let

f(x)=(x+1)^2-1(x \geq-1)

S=\left\{x: f(x)=f^{-1}(x)\right\}