Question

find the inverse of the function and determine whether the inverse is a function: f(x)=7x^2

Answer 1

We know \(y = f(x)\) so:
\(y = 7x^2\)

Now swap \(x\) and \(y\):
\(x = 7y^2\)

Next isolate y:
\(y = \pm\sqrt{\frac{x}{7}}\)

Replace \(y\) with \(f^{-1}(x)\)
\(f^{-1}(x) = \pm\sqrt{\frac{x}{7}}\)

The inverse doesn't appear to be a function since for every x value you get two y values. For a function, every x must produce exactly one y.

Answer 2

thankyou!

Answer 3

Hang on...I was posting a solution and then it cut out.