Functions: Let f and g be two functions defined by f(x)=begincasesx+1, & x<0\\… | JEE Main 2023

JEE Main 2023 (Online) 11th April Evening ShiftQuestion 1

Let $f$ and $g$ be two functions defined by $f(x)=\begin{cases}x+1, & x<0\\ |x-1|, & x\ge0\end{cases}$ and $g(x)=\begin{cases}x+1, & x<0\\ 1, & x\ge0\end{cases}$. Then $(g\circ f)(x)$ is

Functions

differentiable everywherenot continuous at $x=-1$continuous everywhere but not differentiable at $x=1$continuous everywhere but not differentiable exactly at one point✓ Correct answer

Solution

$f(x)<0$ only for $x<-1$, where $(g\circ f)(x)=x+2$; for $x\ge-1$, $(g\circ f)(x)=1$. It is continuous everywhere (value $1$ at $x=-1$) and has a corner only at $x=-1$.

Functions - JEE Mathematics question (JEE Main 2023 (Online) 11th April Evening Shift)

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