Question

Let f(x) = 2x - 6. Solve f-1(x) when x = 2.

So, how would I do this? I'm finding an inverse.

Answer 1

Yes, you have to find the inverse here.

What is the inverse?
It is just another graph g(x) [inverse of f(x)] which is symmetrical to the original graph f(x) about the x = y line.

Here,
f(x) = 2x-6
Let y = 2x-6

Now, represent, 'x' in terms of y.

y + 6 = 2x
x = \(\frac{y+6}{2}\)

Now, switch the variables.

y = \(\frac{x+6}{2}\)
\[f^{-1} (x) = \frac{x+6}{2}\]