Question

For the function f(x) = (3 – 4x)², find f^–1. Determine whether f–1 is a function.
please explain how to do this because i dont understand

Answer 1

http://www.purplemath.com/modules/invrsfcn3.htm

Answer 2

page 5 specifically

Answer 3

http://www.purplemath.com/modules/invrsfcn5.htm

Answer 4

so im doing the inversE?

Answer 5

If the function \(f\) is invertible (i.e. \(f^{-1}\) is a function), then it must be one-to-one i.e. you can solve for a single \(x\) given \(f(x)\). So, without further ado, let's solve for \(x\):$$f(x)=(3-4x)^2\\\pm\sqrt{f(x)}=4x-3\\3\pm\sqrt{f(x)}=4x\\x=\frac{3\pm\sqrt{f(x)}}4$$See that \(\pm\)? That means we have two \(x\) that could give a certain \(f(x)\) and therefore the function is not one-to-one. Thus the function \(f\) is not invertible and \(f^{-1}\) is not a function.

Answer 6

ohh ok thank you very much

Answer 7

The reason I turned \(3-4x\) into \(4x-3\) is because it was easier to deal with... when you square, the original sign doesn't matter, right? Since \(3-4x=-(4x-3)\) that means \((3-4x)^2=(4x-3)^2\).

Answer 8

oh i see what you did thank you