Question

If f(x)=5x-3 then what is f^1(x)?

Answer 1

Do you mean \(f^{-1}(x)\)?

Answer 2

You first multiply 5 to a number, then you subtract 3.
You'd do the exactly opposite thing.
You first add 3, then you divide 3 from the whole.

Answer 3

There's a technical way to do that too.

Answer 4

\( \color{Black}{\Rightarrow f(x) = 5x - 3 \Longrightarrow y = 5x - 3}\)

\( \color{Black}{\Rightarrow y + 3 = 5x}\)

\( \color{Black}{\Rightarrow \Large {y + 3 \over 5} \normalsize = x}\)

Answer 5

As you have solved for \(x \) in terms of \(y\), you may now replace \(x\) with \(f^{-1}(x)\) and \(y \) with \(x\).

Answer 6

That gets you \[ f^{-1}(x) = {x + 3 \over 5}\]