Question

How do you verify if `f(x)=2x-4; g(x)=1/2x+2` are inverse functions?

Answer 1

`"see explanation"`

Explanation:

`"if "f(g(x))=x" and "g(f(x))=x`

`"then they are inverse functions"`

`f(g(x))=f(1/2x+2)`

`color(white)(f(g(x)))=2(1/2x+2)-4`

`color(white)(f(g(x)))=x+4-4=x`

`g(f(x))=g(2x-4)`

`color(white)(g(f(x)))=1/2(2x-4)+2`

`color(white)(g(f(x)))=x-2+2=x`

`rArrf(x)" and "g(x)" are inverse functions"`