Question

Determine the range of the inverse of f(x)=sqrt x-4

Answer 1

First, we need to find the inverse of our function
`f(x)= √(x-4)`. To do that we are going to take advantage of the fact that
`f(x)=y`. So we can rewrite our function as
`y= √(x-4)`; now, we are gong to interchange
`x` and
`y` and solve for
`y` to find our inverse:

`y= √(x-4)`

`x= √(y-4)`

`x^(2) =y-4`

`y= x^(2) +4`
Since this is the parabola
`x^(2)` shifted 4 units upwards. Its range will be [4,∞)