# How do you find the inverse of f(x)= -|x+1|+4?

The function $f \left(x\right)$ does not have an inverse.
Given a function of x such that $y = f \left(x\right)$, the function has an inverse, if and only if, there is one and only one value of x that produces a given value of y.
Except for the point $\left(- 1 , 4\right)$ there are two values of x that produce a given value of y, therefore, there is no inverse.