Question

If f(x) = √5-x, find the inverse function f⁻¹

Answer 1

To find the inverse function of f(x) = √(5-x), switch x and y in the equation and solve for y to obtain f⁻¹(x) = 5 - x², assuming the original function is one-to-one.

Step-by-step explanation:

When finding the inverse function f⁻¹ of a given function f(x) = √(5 - x), we aim to switch the roles of x and y in the equation and then solve for y. Here are the steps:

1. Write the function as y = √(5 - x).
2. Switch x and y to get x = √(5 - y).
3. Square both sides of the equation to get rid of the square root: x² = 5 - y.
4. Rearrange to solve for y: y = 5 - x². So the inverse function f⁻¹(x) = 5 - x².

Note that for the inverse to be a function, the original function must be one-to-one, which depends on the domain of f(x). In this case, we are not given a specific domain for f(x), so we assume it's the domain where f(x) is one-to-one.