Question

How do you find the inverse of `h(x)=(5x+1)/4` and is it a function?

Answer 1

`color(blue)(h^-1(x)=(4x-1)/5`

Explanation:

`h(x)=(5x+1)/4`

To find the inverse we need to express `x` as a function of `y`:

`y=(5x+1)/4`

Multiply by 4:

`4y=5x+1`

Subtract 1:

`4y-1=5x`

Divide by 5:

`(4y-1)/5=x`

Substitute `\ \ \ \ \ \ y=x`:

`y=(4x-1)/5->h^-1(x)=(4x-1)/5`

This is a function. We could verify this with the vertical line test, but, our function `h(x)` is just an equation of a line. These always have an inverse for the whole domain of `h(x)`