Question

Question #95d2b

Answer 1

`f^-1(x)=+-sqrt((x+5)/7)` (In the explanation, we will not use `f^-1(x)` to make things simpler.

Explanation:

`g(x)` is inverse of `f(x)` if `g(f(x))=x`. If this is true, this is also true: `f(g(x))=x`.

Let's call our inverse function `g(x)`
We know that `g(f(x))=x` and that `f(g(x))=x`.

Out of the two, we will use `f(g(x))=x`.
Whatever `g(x)` is, we know that when it is plugged into `f(x)`, it will give us `x`. To make matters simpler, we will call `g(x)` as `y`.

Therefore, we know that `7y^2-5=x` Isolate `y`.
`7y^2-5=x`
`7y^2=x+5`
`y^2=(x+5)/7`
`y=+-sqrt((x+5)/7)`

We see that when these are plugged into `7x^2-5`, it gives us `x`.