Question

How do you find the inverse of `f(x)=x^2+2x-5` and is it a function?

Answer 1

`f^1` does not exist.

Explanation:

Let us recall that, the inverse of a given function exists, if and only if , the given function is a bijection , i.e., the given function is a 1 - 1 ( one-to-one , or, injection ) and onto ( or, surjection ).

Observe that, for the given function `f`, it is not injective, because,

`f(x)=x^2+2x-5=x(x+2)-5`, so that, `f(0)=-5=f(-2)`, meaning that `f` is an `m-1` or, a `many-to-one` and not a `1-1` function.

Hence, `f^1` does not exist.