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JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

If

f(x)=\left\{\begin{array}{ll}x^3+1 & x<0 \\ x^2+1, & x \geq 0\end{array}, g(x)= \begin{cases}(x-1)^{1 / 3}, & x<1 \\ (x-1)^{1 / 2}, & x \geq 1\end{cases}\right.

then

(g \circ f)(x)

is equal to

View answer and explanation

Correct option: A

x, \forall x \in R

Option A (

x, \forall x \in R

) is correct because when you compute

(g \circ f)(x)

for both cases of

f(x)

and

g(x)

, the result simplifies to

x

for all real numbers.

More Questions from FUNCTIONS

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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\}