Find each of the following functions fx 1 3x gx cos xSolut

Find each of the following functions.

f(x) = 1 3x, g(x) = cos x

f(x) = 1-3x g(x) = cosx

i) f o g:

Plug x = g(X) in f(x)

So , f of = 1 - 3cosx

Domain: ( -inf , inf ) All real

ii) (g o f)(x)

Plug x = f(x) in g(x)

(g o f )(x) = cos( 1-3x)

Domain : All real ( -inf , inf)

iii) f o f

Plug x= f(x) in f(x)

f o f = 1 -3( 1-3x) = 1-3 +9x = -2 +9x

Domain : ( -inf, inf) ; All real

iv) g o g

Plug x= g(x) in g(x)

g og = cos(cos3x)

Domain: ( -inf , inf ) All real