Let f, g: R arrow R be defined as : f(x)=|x-1| and g(x)= cases e^x, MARA & x ≥ 0 x+1, & x ≤ 0 cases Then the function f(g(x)) is

Correct answer: A. neither one-one nor onto. aligned & f(g(x))=|g(x)-1| & f o g[ array cc |e^x-1| & x ≥ 0 |x+1-1| & x ≤ 0 array . & fog [ array cc e^x-1 & x ≥ 0 -x & x ≤ 0 array . aligned

JEE Main 20245 AprilEvening Shift

Exam: JEE Main
Year: 2024
Date: 5 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Functions

JEE Main 2024 · 5 April · Evening Shift · Mathematics · Functions

Let f, g: R arrow R be defined as : f(x)=|x-1| and g(x)= cases e^x,...

Let

f, g: \mathbf{R} \rightarrow

\mathbf{R}

be defined as :

f(x)=|x-1|

\text{\text{ and } }

g(x)=

\begin{cases}\mathrm{e}^x, \text{ MARA } & x \geq 0 \\ x+1, & x \leq 0\end{cases}

<br />Then the function

f(g(x))$ is

Options

Aneither one-one nor onto.
Bone-one but not onto.
Conto but not one-one.
Dboth one-one and onto.

Correct answer

A. neither one-one nor onto.

Step-by-step solution

\begin{aligned} & f(g(x))=|g(x)-1| \\ & f o g\left[\begin{array}{cc}\left|e^x-1\right| & x \geq 0 \\ |x+1-1| & x \leq 0\end{array}\right. \\ & \text{ fog }\left[\begin{array}{cc}e^x-1 & x \geq 0 \\ -x & x \leq 0\end{array} \right.\end{aligned}

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