Question

When given f(x)=3x+12, find f(f^-1(x))

Answer 1

`\large\boxed{f\bigg(f^(-1)(x)\bigg)=x}`

Explanation:

`\text{Find}\ f^(-1)(x)`

`f(x)=3x+12\to y=3x+12`

exchange x to y and vice versa:

`x=3y+12`

solve for y:

`3y+12=x` subtract 12 from both sides

`3y=x-12` divide both sides by 3

`y=(x-12)/(3)\to f^(-1)(x)=(x-12)/(3)`

`f\bigg(f^(-1)(x)\bigg)\to` replace x in f(x) with the expression
`(x-12)/(3)`

`f\bigg(f^(-1)(x)\bigg)=3\cdot(x-12)/(3)+12=x-12+12=x`