Question

For the function f(x)=f(x)=(7-8x)^2, find f^-1. Determine whether f^-1 is a function.

Answer 1

To find the inverse of a function, consider:
\[y = (7-8x)^{2}\]
Now find x as a function of y from the above equation.(as in x = f(y))

Answer 2

Let the equation you get once you do that be x = g(y). Then g(y) is the inverse, i.e.,
\[g(y) = f ^{-1} (y)\]
To check if its a function, plot its graph and check whether at any point there are two values of y for a single value of x.

Answer 3

Here is an example of something similar.

\(f(x) = x^2-1\)

First make it \(y=x^2-1\) and now solve in terms of \(x\)

\(y+1=x^2\implies x=\pm\sqrt{y+1}\)

Surely this is not a function as we get two answers for every \(y>-1\)