Question

f(x) be a differentiable function such that f'(x) = log1/3(log3(sinx + a)). If f(x) is decreasing for all real values of x, find a.

Answer 1

Since f(x) be a decreasing function, we have log1/3(log3(sinx + a)) < 0

⇒ (log3(sin x + a)) > 1

⇒ (sin x + a) >3

⇒ a > 3 – sinx

⇒ a > 4 for all x in R.