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

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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, ∞]
asked Jan 29, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The function is .

Differentiate on each side with respect to image.

Apply power rule in derivatives image.

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 .

answered Jan 31, 2015 by david Expert
edited Jan 31, 2015 by david

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