Final answer:
The inverse of a function is a function that reverses the original function's effect. To find it algebraically, swap the variables and solve for the new dependent variable. It fulfills the condition that applying the original function to its inverse returns the input value.
Step-by-step explanation:
When you are looking to find the inverse of a function or operation in mathematics, you are essentially looking for a way to reverse the effects of that function or operation. For example, the inverse of addition is subtraction, having the property that if you add a number to another and then subtract the same number, you are back to the original number. If we are dealing with a mathematical function, say f(x), the inverse function, typically denoted as f-1(x), would be the function that fulfills the condition that f(f-1(x)) = x for all x in the domain of f-1.
To find the inverse of a function algebraically, you often interchange the roles of x and y and solve for y. For example, if you have a function f(x) = 2x + 3, to find its inverse, you would write y = 2x + 3, swap x and y to get x = 2y + 3, and then solve for y to find the inverse function f-1(x).