Question

If f(x) = √(|x – 1|) and g(x) = sinx, then calculate (f_og)(x) and (g_of)(x) and discuss the differentiability of (g_of)(x) at x = 1.

Answer 1

We have (fog)(x)

= f(g(x))

= f(sin x)

= √(|sinx – 1|)

Also, (g_of)(x)

= g(f(x)) = g(√(|x – 1|))

= (√(sin|x – 1|))

Clearly, (g_of)(x) is not differentiable at x = 1.