The function f(x)= x^4 is not one-to-one. Find a suitable restriction on the domain of f so that the new function that results is one-to-one. Then find the inverse of f.

Restrict it to be non-negative to meet the 1-1 requirement.

To restrict the function f(x) = x^4 to make it one-to-one, we need to limit the domain to ensure that each output value (range) corresponds to a unique input value. Since the original function is not one-to-one, we can restrict the domain to be non-negative, meaning x ≥ 0.

By limiting the domain to x ≥ 0, the function f(x) = x^4 becomes one-to-one because any non-negative number raised to the power of 4 will always result in a non-negative output. Therefore, each input value corresponds to a unique output value.

To find the inverse of the restricted function, we can follow these steps:

1. Replace f(x) with y: y = x^4
2. Swap x and y: x = y^4
3. Solve for y: y = ∛x, where ∛ denotes the cube root.

Therefore, the inverse function of f(x) = x^4, within the restricted domain of x ≥ 0, is g(x) = ∛x.

Note: The inverse function g(x) = ∛x is only valid when x is non-negative (x ≥ 0).