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Limits Continuity and Differentiability question

2023 · 11 Apr · Shift 2 · Q33

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JEE Main
Mathematics
Limits Continuity and Differentiability
2023 · 11 Apr · Shift 2 · Q33

Limits Continuity and Differentiability question

2023 · 11 Apr · Shift 2 · Q33

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

f

and

g

be two functions defined by

f(x)=\left\{\begin{array}{cc}x+1, & x \lt 0 \\ |x-1|, & x \geq 0\end{array}\right.

and

g(x)=\left\{\begin{array}{cc}x+1, & x \lt 0 \\ 1, & x \geq 0\end{array}\right.

Then

(g \circ f)(x)

is :

A
continuous everywhere but not differentiable at $x=1$
B
differentiable everywhere
C
not continuous at $x=-1$
D
continuous everywhere but not differentiable exactly at one point

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