Question

Urgent
I need the step by step on how to get this, I really appreciate it

Answer 1

The inverse of f(x) is g(y)=
`((y-8)^(2))/(4)+4`

Explanation:

Given function is given by f(x)=
`2√(x-4) +8`

Let, y=f(x)=
`2√(x-4) +8`

and g(y)=x is inverse of f(x)

Now,

f(x)=
`2√(x-4)+8`

y=
`2√(x-4)+8`

y-8=
`2√(x-4)`

`(y-8)/(2)=√(x-4)`

`((y-8)^(2))/(4)=(x-4)`

`((y-8)^(2))/(4)+4=x`

`((y-8)^(2))/(4)+4=x`

g(y)=x=
`((y-8)^(2))/(4)+4`

Thus, the inverse of f(x) is g(y)=
`((y-8)^(2))/(4)+4`