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

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

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

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$\frac{1}{{1.2}} + \frac{1}{{2.3}} + \frac{1}{{3.4}} + ........ + .......\frac{1}{{n.(n + 1)}}$ equals

If $\frac{{dy}}{{dx}} + \frac{1}{{\sqrt {1 - {x^2}} }} = 0$, then

Consider the triangles with vertices $A (2,1) B (0,0)$ and $C ( t , 4), t \in[0,4]$. It the maximum and the minimum perimeters of such triangles are obtained at $t=\alpha$ and $t=\beta$ respectively, then $6 \alpha+21 \beta$ is equal to $.........$.

$\int_{}^{} {\frac{{dx}}{{5 + 4\cos x}} = } $

At which points the function$f(x) = \frac{x}{{[x]}}$, where$[.]$ is greatest integer function, is discontinuous

Direction ratios of the normal to the plane passing through the points $(0, 1, 1), (1, 1, 2)$ and $(-1, 2, -2)$ are

A real root of the equation ${\log _4}\{ {\log _2}(\sqrt {x + 8} - \sqrt x )\} = 0$ is

The mean of five observations is $5$ and their variance is $9.20$. If three of the given five observations are $1, 3$ and $8$, then a ratio of other two observations is

The product of all real roots of the equation ${x^2} - |x| - \,6 = 0$ is

If $x$ be real, the least value of ${x^2} - 6x + 10$ is