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

1 Answer
Apr 18, 2018

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)