Question

If f(x) = sin x + cos x, g(x) = x² – 1, then g(f(x)) is invertible in the domain

(a) [ 0, π/2]

(b) [ – π/4, π/4]

(c) [ – π/2, π/2]

(d) [0, π]

Answer 1

Correct option (b) [– π/4, π/4]

Explanation:

Given f(x) = sinx + cosx, g(x) = x² – 1

Now, g(f(x)) = (sinx + cosx)² –1

= sin2x

Clearly g(f(x)) is invertible in the domain of