Question

Guys, help me please! find the inverse function

If f(x) = 2x ÷ 3 and g(x) = 3x + 4, what is g-1[f(x)] if x = 9?

Answer 1

Explanation:

Answer is 5

Answer 2

`g^(-1)[f(9)]=(2)/(3)`

Explanation:

To find
`g^(-1)(x)`

instead of g, we write y

`y=3x+4`

swap x's and y's

`x=3y+4`

make y subject of the expression

`y=(x-4)/(3)\\\implies g^(-1)(x)=(x-4)/(3)`

`g^(-1) \[f(x)\]\quad \textnormal{means put}\quad f \quad \textnormal{in to }\quad g^(-1)`

`\therefore g^(-1)[f(x)]=((2x)/(3)-4)/(3)`

`=(2x-12)/(9)`

if
`x=9`

`g^(-1)[f(9)]=(2(9)-12)/(9)=(18-12)/(9)=(6)/(9)=(2)/(3)`