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

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Answer 1 · 2017-12-13T03:40:26

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.

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