Question

For $xϵR,f\left(x\right)=|log2-sinx|andg\left(x\right)=f\left(f\right(x\left)\right)$ then:

• A. g’(0) = cos(log 2)
• B. g’(0) = -cos(log 2)
• C. g is differentiable at x = 0 and g’ (0) = -sin(log 2)
• D. g is not differentiable at x = 0

Answer 1

The correct option is A

g’(0) = cos(log 2)

g(x) =f(f (x)) = | log2 - sin | log2 - sin x ||

g(x) = f(f(x)) = log2 – sin(log2 – sinx)

g’(x) = -cos(log2 – sinx).(– cosx)

g’ (0) = cos(log2)