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

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