Find the inverse of the function ? f(x) = x^2*sin(1/x) for x≉0 .
1 Answer
The function does not have an inverse.
Explanation:
In order for a function to have an inverse, it must be injective. As we remember, a function
For example, let's have the following function, portrayed through diagrams:
This function is not injective, because
On the other hand, the one below
is an injective function.
The reason why a function is inversible only if it is injective is due to the definition of functions. A function is a valid function if and only if there exists no
If there exists
For our function,
Thus,