Question

(PLEASE ANSWER)

For f(x) = 4x + 3 and g(x) = 9x find the following composite functions and state the domain of each
(a) f o g (b) g o f (c) f o f (d) g o g
(a) (f o g)(x) =

Answer 1

Answer: a) 36x + 3

b) 36x + 27

c) 16x + 15

d) 81x

Explanation:

f(x) = 4x + 3 g(x) = 9x

a) f(g(x)) = 4(9x) + 3 replaced x in f(x) equation with 9x

= 36x + 3

b) g(f(x)) = 9(4x + 3) replaced x in g(x) with 4x + 3

= 36x + 27

c) f(f(x)) = 4(4x + 3) + 3 replaced x in f(x) with 4x + 3

= 16x + 12 + 3

= 16x + 15

d) g(g(x)) = 9(9x) replaced x in g(x) with 9x

= 81x

Answer 2

solution given:

f(x) = 4x + 3

g(x) = 9x

answer:

a.fog(x)=f(9x)=4×9x+3=36x+3

domain=real number

b.gof (x)=g(4x+3)=9(4x+3)=36x+26

domain=real number

c.fof(x)=f(4x+3)=4(4x+3)+3=16x+12+3

=16x+15

domain: real number

d.

gog(x)=g(9x)=9×9x=81x

domain: real number.