Question

Given: F(x) = 5x - 6 and G(x) = x - 4

G -1 F -1 =

(x + 26)/5

-6x + 10

(x + 10)/5

Answer 1

1st answer

Explanation:

find inverses

then plug in g^-1(f^-1(x)

Answer 2

Correct choice is
`(x+26)/(5)`

Explanation:

1. If
`F(x)=5x-6,` then you can find the inverse
`F^(-1)(x):`

`y=5x-6,\\ \\5x=y+6,\\ \\x=(y+6)/(5),\\ \\F^(-1)(x)=(x+6)/(5).`

2. If
`G(x)=x-4,` then

`y=x-4,\\ \\x=y+4,\\ \\G^(-1)(x)=x+4.`

3. Hence,

`G^(-1)(F^(-1)(x))=G^(-1)\left((x+6)/(5)\right)=(x+6)/(5)+4=(x+26)/(5).`