For fx x 5 and gx 5x 2 find the following functions f ord

For f(x) =x + 5 and g(x) = 5x + 2, find the following functions. (f ordm g)(x); (g ordm f)(x); (f ordm g)(1) (g ordm f)(1)

Solution

f(x) = x+5 ; g(x) = 5x +2

a) ( f og )(x)

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

( f og )(x) = 5x +2 +5 = 5x +7

b) ( g o f)(x)

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

( g o f)(x) = 5(x +5) +2

= 5x + 27

c) (f o g)(1) = 5*1 +7 = 12

d) ( g o f)(x) = 5(1) +27 = 32