Question

Can someone help me with this? Thank you

Answer 1

a.) (f o g)(4)= 11

b.) (g o f)(4)= 16

c.) (f o g)(x)= 2
`x^(2)`-21

d.) (g o f)(x)= 4
`x^(2)`-12x

Explanation:

a.) (f o g)(4)=

(f(g(4))

f(
`4^(2)`-9)

2(
`4^(2)`-9)-3

2(7)-3

11

b.) (g o f)(4)=

(g(f(4))

g(2(4)-3)

`(2(4)-3)^(2)`-9

`(8-3)^(2)`-9

`5^(2)`-9

25-9

16

c.) (f o g)(x)=

(f(g(x))

f(
`x^(2)`-9)

2(
`x^(2)`-9)-3

2
`x^(2)`-18-3

2
`x^(2)`-21

d.) (g o f)(x)=

(g(f(x))

g
`(2x-3)^(2)`

`(2x-3)^(2)`-9

(2x-3)(2x-3)-9

4
`x^(2)`-12x+9-9

4
`x^(2)`-12x