Question

Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval.

f (x) = (x - 4)^2,        [4, ∞]

Answer 1

Step 1:

The function is .

Differentiate on each side with respect to .

Apply power rule in derivatives .

Apply chain rule in derivatives.

on .

The derivative is always positive on therefore is increasing and thus has an inverse on this interval.

is positive on the domain of .

is strictly monotonic and it must have inverse function.

Solution:

on .