×

Hello! Socratic's Terms of Service and Privacy Policy have been updated, which will be automatically effective on October 6, 2018. Please contact hello@socratic.com with any questions.

How do you find the inverse of #y = - |x-3| + 5#?

1 Answer
Dec 13, 2017

Answer:

We have #color(red)(y = - |x-3| + 5)#

The Inverse of this function is #color(red)(x = - |y-3| + 5)#

Graph with the function and it's inverse is available with this solution.

Explanation:

We have #color(blue)(y = - |x-3| + 5)# ... Equation.1

To find the inverse of this function,

Switch #color(red)x# with #color(red)y# and #color(blue)y# with #color(blue)x# to obtain

#color(blue)(x = - |y-3| + 5)# ... Equation.2

A few observations .....

The Inverse of f(x) does not pass the Vertical Line Test and hence is NOT a function

The graph of the inverse of f(x), reflects the graph of y = f(x) , across the line #color(green)(y = x#

The graph with f(x) and it's inverse is available below:

enter image source here