JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

Let

f:[0,1] \rightarrow[0,1]

and

g:[0,1] \rightarrow[0,1]

be two functions defined by

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

and

g(x)=4 x(1-x)

then

(f \circ g)(x)

is equal to

View answer and explanation

Correct option: C

\frac{1-4 x+4 x^2}{1+4 x-4 x^2}

Option C (

\frac{{1-4 x+4 x^2}}{{1+4 x-4 x^2}}

) is correct because it is the result of substituting g(x) into f(x) and simplifying the expression.

More Questions from FUNCTIONS

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

f(x)=x(4-x)

f^{-1}(x)

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

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

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