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MCQMediumJEE Main 2023 · 11 April, Shift 2Composition & Inverse Functions

Mathematics Question from JEE Main 2023 · 11 April, Shift 2

Let ff and gg be two functions defined by:

f(x)={x+1,x<0∣x−1∣,x≥0,g(x)={x+1,x<01,x≥0.f(x) = \begin{cases} x + 1, & x < 0 \\ |x - 1|, & x \geq 0 \end{cases}, \quad g(x) = \begin{cases} x + 1, & x < 0 \\ 1, & x \geq 0 \end{cases}.

Then (g∘f)(x)(g \circ f)(x) is:

  • A

    continuous everywhere but not differentiable at x=1x = 1

  • B

    continuous everywhere but not differentiable exactly at one point

  • C

    differentiable everywhere

  • D

    not continuous at x=−1x = -1

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