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)#