QJEEM24Ma3d4b: JEE Main 2024 Mathematics - Class 11 JEEM24Ma3d4b Solution: Let f , g : R → R be defined as : f ( x ) =

Question

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QJEEM24Ma3d4b: JEE Main 2024 Mathematics - Class 11 JEEM24Ma3d4b Solution: Let f , g : R → R be defined as : f ( x ) =

Let $f, g : R \to R$ be defined as :

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

Then the function $f (g (x))$ is

Multiple Choice Options

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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Accepted Answer

$\begin{aligned} f (x) = {\begin{cases} x - 1, & x \geq 1 \\ 1 - x & x < 0 \end{cases} \\ g (x) = {\begin{array}{cc} e^{x} & ; x \geq 0 \\ x + 1 & ; x \leq 0 \end{array} \end{aligned}$

JEE Main 2024 (Online) 5th April Evening Shift Mathematics - Functions Question 12 English Explanation 1

$\begin{aligned} f (g (x)) & = {\begin{cases} g (x) - 1, & g (x) \geq 1 \\ 1 - g (x) & g (x) < 1 \end{cases} \\ = {\begin{array}{cl} e^{x} - 1 & x \geq 0 \\ - x & x < 0 \end{array} \end{aligned}$

JEE Main 2024 (Online) 5th April Evening Shift Mathematics - Functions Question 12 English Explanation 2

QJEEM24Ma3d4b: JEE Main 2024 Mathematics - Class 11 JEEM24Ma3d4b Solution: Let f , g : R → R be defined as : f ( x ) =

Multiple Choice Options

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