Please see attached.
I am not sure whether my example of this function is correct.
f(x) = ##sin(\frac{\pi x}{2})##
obviously, f(x) is continuous on [-1,1] and differentiable on (-1,1)
Inverse of f(x) will be ##\frac{2 sin^{-1}x}{\pi} ##
and d/dx (inverse of f(x)) will be ##\frac{2}{π \sqrt{1-x^2}}##
So not differentiable in -1,1 ??
I am not sure whether my example of this function is correct.
f(x) = ##sin(\frac{\pi x}{2})##
obviously, f(x) is continuous on [-1,1] and differentiable on (-1,1)
Inverse of f(x) will be ##\frac{2 sin^{-1}x}{\pi} ##
and d/dx (inverse of f(x)) will be ##\frac{2}{π \sqrt{1-x^2}}##
So not differentiable in -1,1 ??
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