Question

How do you show that `f(x)=3-4x` and `g(x)=(3-x)/4` are inverse functions algebraically and graphically?

Answer 1

See proof below

Explanation:

To show that 2 functions are inverses, we calculate

`f(f^-1(x))` ant this is `=x`

Here, we have

`f(x)=3-4x`

`g(x)=(3-x)/4`

`f(g(x))=f((3-x)/4)=3-(4*(3-x)/4)=3-3+x=x`

`g(f(x))=g(3-4x)=(3-(3-4x))/4=(3-3+4x)/4=x`

Therefore,

`f(x)` and `g(x)` are inverses.

`QED`

Graphically, 2 functions are inverses if they are symmetric with respect to the line `y=x`

graph{(y-3+4x)(4y-3+x)(y-x)=00 [-3.7, 4.095, -0.95, 2.945]}