Let f : R → R : f(x) = x 2, g : R → R : g(x) = tan x and h : R → R : h(x) = log x. Find a formula for h o (g o f). Show that [h o (g o f)]

Question

Philoid · Accepted Answer

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To find: formula for h o (g o f)

To prove:

Formula used: f o f = f(f(x))

Given: (i) f : R → R : f(x) = x²

(ii) g : R → R : g(x) = tan x

(iii) h : R → R : h(x) = log x

Solution: We have,

h o (g o f) = h o g(f(x)) = h o g(x²)

= h(g(x²)) = h (tan x²)

= log (tan x²)

h o (g o f) = log (tan x²)

For,

= 0

Hence Proved.