Inverse function

Question

determine whether the function has an inverse function.

Answer 1

This function is not one-to-one function as even function and because it has not inverse on all domain (x ≠ 0)

Answer 2

This is a bit of a trick question, This function is NOT one-to-one. In other words, it does not pass the horizontal line test. Consequently, the inverse will not pass the vertical line test so the inverse will not be a function UNLESS the domain is restricted.

So, the only way to get the inverse to be a function is to restrict the domain.

To find the inverse:

Step 1: Replace h(x) with "y":

y = -3/x²

Step 2: Swap the "x" and "y":

x = -3/y²

Step 3: Solve for "y"

y²x = -3

y² = -3/x

y = ±√(-3/x)

But, because this is ±, it is not a function. To be a function, you must restrict the domain to either

f^-1(x) = -√(-3/x) or f^-1(x) = √(-3/x)

But the short answer is that the inverse is not a function.