MCQ
If $f(x) = max(sinx, sin^{-1}(cosx))$, then
- ✓$ƒ$ is continuous everywhere
- B$ƒ$ is discontinuous at $1$ point
- C$ƒ$ is discontinuous at $2$ points
- D$ƒ$ is discontinuous at infinitely many
✓
Answer
Correct option: A.
$ƒ$ is continuous everywhere
a
Given, $f(x)=\max \sin x, \sin ^{-1}(\cos x)$
Given, $f(x)=\max \sin x, \sin ^{-1}(\cos x)$
$g(x)=\sin ^{-1}(\cos x)=\left\{\begin{array}{ll}\pi / 2-x & 0<x<\pi \\ \pi / 2+x & -\pi<x<0\end{array}\right.$
$n(x)=\sin x$
Plotting on graph from graph, it is clear that $f(x)$ is continuous everywhere, Hence, shape points are not differentiable
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