For fx 10x and gx 110 x find f o gx and g o fx Then determ

For f(x) = 10x and g(x) = 1/10 x, find (f o g)(x) and (g o f)(x). Then determine whether (f o g)(x) = (g o f)(x). What is (f o g)(x)? (f o g)(x) =

Solution

f(x) = 10x

g(x) = x/10

(fog)(x) : plug x = g(x) in f(x)

( f o g)(x) = 10(x/10) = x

( g o f )(x) : plug x = f(x) in g(x)

(g o f )(x) = (10x)/10 = x

Yes ( f o g)(x) = (g o f )(x)

(f o g )(x) = x