Question

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For the function f(x) = (3 – 4x)², find f^–1. Determine whether f^–1 is a function.

Answer 1

To get the inverse function you would graphically flip the function over the line y=x.

The easiest way to do this would be to exchange the positions of x and y, and then solve for y. So you have\[y=(3-4x)^{2}\]And to get the inverse just solve\[x=(3-4y)^{2}\]for y.

As for determining whether or not the inverse function exists, apply the horizontal line test to the original function: Any horizontal line you could possible draw should only cross the function at a single place.

Answer 2

So it is a functioon if I did the line test right.

Answer 3

Well, no.

The function will be parabolic, so for example the value of y=1 corresponds to both x=1 and x=.5

Answer 4

Ok thanks!