Question

For f(x) = 5x and g(x)= x + 9, find

(fog)(x); b. (gof)(x); (fog)(3)
a.
C.
a.
(fog)(x)=
(Simplify your answer.)

Answer 1

• (fog)(x) = 5x+45

• (gof)(x) = 5x+9

• (fog)(3) = f(g(3)) = f(12) = 60

Explanation:

Given

• f(x) = 5x

• g(x) = x + 9

Finding (fog)(x)

(fog)(x) = f(g(x))

(fog)(x) = f(x+9)

(fog)(x) = 5(x+9) ∵ substitute x as x+9 in the f(x)

(fog)(x) = 5x+45

Finding (gof)(x)

(gof)(x) = g(f(x))

(gof)(x) = g(5x)

(gof)(x) = 5x+9 ∵ substitute x as 5x in the g(x)

Finding (fog)(3)

(fog)(3) = f(g(3))

substitute x = 3 in the g(x)=x+9

g(x) = x+9

g(3) = 3+9

g(3) = 12

so

(fog)(3) = f(g(3)) = f(12)

now substitute x = 12 in f(x) = 5x

f(x) = 5x

f(12) = 5(12)

f(12) = 60

Thus,

(fog)(3) = f(g(3)) = f(12) = 60