What is the inverse function ?

Question

What is the inverse function of y=-4|x+2|+5

Answer 1

What is the inverse function of y=-4|x+2|+5

-4|x + 2| = y - 5

|x + 2| = -1/4 (y - 5)

x + 2 = ±1/4 (y - 5)

x = ±1/4 (y - 5) - 2

Answer 2

The absolute value function is v-shaped and is not one-to-one, so it doesn't have an inverse.

If you restrict domain say to x>=-2, then this part is one-to-one and has a inverse.

To find it, "open" the absolute value bars with the sign "+"

y = -4 (x+2) + 5

Swap X and Y

x = -4(y+2) + 5

And solve for Y:

y+2 = (x-5)/(-4)

y = -0.25 x - 0.75 with the restriction on domain x<=5