Question

How do you tell if inverse of function exist.

Answer 1

Inverse of function:

If a horizontal line intersects the original function in a single point, then the function is a one-to-one function and inverse is also a function.

For Example;

(A) Let $f\left(x\right)=x^3$ be a function

Now, Check if this function has an inverse by horizontal line test

It passes the horizontal line test.

So, $f\left(x\right)=x^3$ has an inverse function.

(B) Let $f\left(x\right)=x^2$ be a function

Now, Check if this function has an inverse by horizontal line test

It fails the horizontal line test.

So, $f\left(x\right)=x^2$ does not have an inverse function.

Hence, you can apply the horizontal line test to verify whether a function is a one-to-one function.