Question

How do you find the inverse of `f(x)=(7/x)-3`?

Answer 1

`f^-1(x)=7/(x+3`

Explanation:

Given that `f(x)=7/x-3`
We know that if `f(x)=y` then `f^-1(y)=x`

So, from the main equation, by rearranging we get
`y=7/x-3\impliesy+3=7/x\implies(y+3)/7=1/x`
`:.x=7/(y+3)`

We know what `x` is, so now you know why the answer above is right. (Just replace `y` to `x`)