Let f : R → R : f(x) = x2, g : R → R : g(x) = tan xand h : R → R

1.	Let f : R → R : f(x) = x2, g : R → R : g(x) = tan xand h : R → R : h(x) = log x.Find a formula for h o (g o f).Show that [h o (g o f)] \(\sqrt{\frac{\pi}{4}}=0\)
Answer» To find: formula for h o (g o f) To prove: Show that [h o (g o f)] \(\sqrt{\frac{\pi}{4}}=0\) 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, [h o (g o f)] \(\sqrt{\frac{\pi}{4}}=0\) \(=log[tan(\frac{\pi}{4}^2)]\) \(=log[tan\frac{\pi}{4}]\) = log 1 = 0 Hence Proved.

Let f : R → R : f(x) = x2, g : R → R : g(x) = tan xand h : R → R : h(x) = log x.Find a formula for h o (g o f).Show that [h o (g o f)] \(\sqrt{\frac{\pi}{4}}=0\)

Answer»

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

To prove: Show that [h o (g o f)] \(\sqrt{\frac{\pi}{4}}=0\)

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, [h o (g o f)] \(\sqrt{\frac{\pi}{4}}=0\)

\(=log[tan(\frac{\pi}{4}^2)]\)

\(=log[tan\frac{\pi}{4}]\)

= log 1

= 0

Hence Proved.