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

Dec 13, 2017

We have $\textcolor{red}{y = - | x - 3 | + 5}$

The Inverse of this function is $\textcolor{red}{x = - | y - 3 | + 5}$

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

#### Explanation:

We have $\textcolor{b l u e}{y = - | x - 3 | + 5}$ ... Equation.1

To find the inverse of this function,

Switch $\textcolor{red}{x}$ with $\textcolor{red}{y}$ and $\textcolor{b l u e}{y}$ with $\textcolor{b l u e}{x}$ to obtain

$\textcolor{b l u e}{x = - | y - 3 | + 5}$ ... 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: