Question

F(X) = 3x
g(X) =x-1

find fg (X) and gf (X)

Answer 1

(f∘g)(x) = f(g(x)) = 3x - 3

(g∘f)(x) = g(f(x)) = 3x - 1

Explanation:

The question should read

f(x) = 3x

g(x) =x-1

find (f∘g)(x) and (g∘f)(x)

∘ is U+2218 RING OPERATOR

In this case it is read "composed with".

To find (f∘g)(x) = f(g(x)), substitute g(x) for x in formula for f(x). Then substitute the formula for g(x).

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

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

Answer 2

see explanation

Explanation:

to evaluate f(g(x)) substitute x = g(x) into f(x), that is

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

Similarly to evaluate g(f(x)) substitute x = f(x) into g(x)

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