Question

How do you find the inverse of `f(x)= -|x+1|+4` and is it a function?

Answer 1

`x=+-|y-4|-1`

Explanation:

`y=f(x)<=4`
The given relation creates 2-1 mapping.. For a given y, there are two values of x, from the equivalent bifurcated equations
`y=+-(x=1)+4`

For the inverse, solve for x, from there equations.

`x= 3-y=(4-y)-1 and x=-(4-y)-1`

to be combined as

`x= +-|y-4|-1`

Care has been taken to prefix both signs to `|y-4|`, to include all x values, permitted by the given equation. This would combine both `x>=-1` (for + sign) and `x<=-1` (for`-`sign).

Anyway, the graph is a `^^`-like right angle at (-1, 4) that is bisected by x = -1.