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Functions question

2024 · 5 Apr · Shift 2 · Q32

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PYQ Library
JEE Main
Mathematics
Functions
2024 · 5 Apr · Shift 2 · Q32

Functions question

2024 · 5 Apr · Shift 2 · Q32

JEE MainMathematicsFunctionsMCQ+4 / −1

Let

f, g: \mathbf{R} \rightarrow \mathbf{R}

be defined as :

f(x)=|x-1| \text { and } g(x)= \begin{cases}\mathrm{e}^x, & x \geq 0 \\ x+1, & x \leq 0 .\end{cases}

Then the function

f(g(x))

is

A
neither one-one nor onto.
B
one-one but not onto.
C
both one-one and onto.
D
onto but not one-one.

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