Question

How do you show that `f(x)=x-5` and `g(x)=x+5` are inverse functions algebraically and graphically?

Answer 1

`"see explanation"`

Explanation:

`"using "color(blue)"composition of functions"`

`• " if "f(g(x)=x" and "g(f(x))=x`

`"then "f(x)" and "g(x)" are inverse functions"`

`f(g(x))=f(x+5)=x+5-5=x`

`g(f(x))=g(x-5)=x-5+5=x`

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

`color(blue)"graphically"`

`"if "f(x)" and "g(x)" are reflections of each other in the line"`
`y=x" then they are inverse functions"`

`"any point "(a,b)" on " f(x)" should correspond to "(b,a)`
`"on "h(x)`
graph{(y-x+5)(y-x-5)(y-x)=0 [-10, 10, -5, 5]}