Increasing Decreasing Function g(x) (Jee Mains)

Application of Derivates

Medium

Increasing Decreasing Function g(x)

Let f : R → R be a twice differentiable function such that f"(x) > 0 for all x∈R and f ' (a – 1) = 0, where a is real number. Let g(x) = f (tan²x – 2tan x + a), 0 < x < $\frac{\pi }{2}$ .
Consider the following two statements :
(I) g is increasing in $\left( {0,\frac{\pi }{4}} \right)$
(II) g is decreasing in $\left( {\frac{\pi }{4},\frac{\pi }{2}} \right)$
Then,

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