fx=tan xftan-1x=tan tan-1x=x _______1gfx=fx-π4= tan x-π4Use tan x-y=tan x- tan y1+ tan x tan ygfx=tan x- tan π41+ tan x tan π4 gfx=tan x-11+ tan x since tan π4=1Put x= tan-1xgftan tan-1x=tan tan-1x-11+ tan tan-1xFrom equation 1gx=x-11+xfgx=tan gx=tan x-11+x

Solve this:

f (x) = \tan x f (\tan^{- 1} x) = \tan (\tan^{- 1} x) = x_______(1) g (f (x)) = f (x - \frac{π}{4}) = \tan (x - \frac{π}{4}) U s e \tan (x - y) = \frac{\tan x - \tan y}{1 + \tan x \tan y} g (f (x)) = \frac{\tan x - \tan \frac{π}{4}}{1 + \tan x \tan \frac{π}{4}} g (f (x)) = \frac{\tan x - 1}{1 + \tan x} \{\sin c e \tan \frac{π}{4} = 1\} P u t x = \tan^{- 1} x g (f (\tan (\tan^{- 1} x))) = \frac{\tan (\tan^{- 1} x) - 1}{1 + \tan (\tan^{- 1} x)} F r o m e q u a t i o n 1 g (x) = \frac{x - 1}{1 + x} f (g (x)) = \tan g (x) = \tan (\frac{x - 1}{1 + x})

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