Let f(x) = * 20 c , , , , , , , , x, & for , , x 0 1 - x, & for ,… - Vidyadip

MCQ

Let $f(x) = \left\{ {\begin{array}{*{20}{c}}{\,\,\,\,\,\,\,\,\sin x,}&{{\rm{for\,\, }}x \ge 0}\\{1 - \cos x,}&{{\rm{for\,\, }}x \le 0}\end{array}} \right.$ and $g(x) = {e^x}$. Then $(gof)'(0)$ is

A
$1$
B
$-1$
✓
$0$
D
None of these

✓

Answer

Correct option: C.

$0$

c
(c) $(gof)\,(x) = g[f(x)] = g\,[1 - \cos x] = {e^{1 - \cos x}},{\rm{ for\,\, }}x \le 0$

$(gof)'(x) = {e^{1 - \cos x}}.\sin x,\,{\rm{for\,\, }}x \le 0$

$(gof)'(0) = 0$.

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