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Functions question

2024 · 1 Feb · Shift 1 · Q41

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PYQ Library
JEE Main
Mathematics
Functions
2024 · 1 Feb · Shift 1 · Q41

Functions question

2024 · 1 Feb · Shift 1 · Q41

JEE MainMathematicsFunctionsMCQ+4 / −1

Let

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

and

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

be defined as

f(x)=\left\{\begin{array}{ll}\log _{\mathrm{e}} x, & x\gt 0 \\ \mathrm{e}^{-x}, & x \leq 0\end{array}\right.

and

g(x)=\left\{\begin{array}{ll}x, & x \geqslant 0 \\ \mathrm{e}^x, & x\lt 0\end{array}\right.

. Then, gof :

\mathbf{R} \rightarrow \mathbf{R}

is :

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

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