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

1 Answer
Eddie
Feb 9, 2017

f^(-1)(x) = 3 pm (5 - x)

Explanation:

y = -|x-3| + 5

|x-3| = 5 - y

x-3 = pm (5 - y)

x = 3 pm (5 - y)

The inverse function is therefore:

f^(-1)(x) = 3 pm (5 - x)

There would be no harm in verifying this for x = 2 and x = 4, ie either side of x = 3 which is the point at which (x-3) changes sign.

For x = color(red)(2), we get y = 4. Our inverse function suggests that f^(-1)(4) = 3 pm 1 = 4, color(red)(2).

And for x = color(blue)(4), we also get y = 4, which we expect from the symmetry. Our inverse function suggests that f^(-1)(4) = 3 pm 1 = color(blue)(4),2.

graph{y = -|x-3| + 5 [-10, 10, -5, 5]}

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