Question

Write the inverse using the notation f^-1(x)
f(x)=x+7/2

Answer 1

Ok, the way I like to do inverses is to remember that \(f(f^{-1}(x)) = x\)

So that means you take the original equation. And swap the x with \(f^{-1}(x)\) and the f(x) with x.

Answer 2

Then you solve it for \(f^{-1}(x)\)

Answer 3

f^-1(x)=2x-7 ?

Answer 4

\(x = f^{-1}(x) + \frac{7}{2}\)\[\implies f^{-1}(x) = x - \frac{7}{2}\]

Answer 5

Just subtract 7/2 from both sides.

Answer 6

Does that make sense? Do you follow what I did there?

Answer 7

Yes, thanks!