To find the inverse of the function f(x) = x², we first need to understand what it means to find an inverse function. The inverse function essentially reverses the operations of the original function.
1. **Switch x and y**: Start by replacing f(x) with y. So we have:
y = x²
Now, we switch the roles of x and y:
x = y²
2. **Solve for y**: Next, we solve this equation for y:
y = √x
3. **Consider the domain**: However, since the original function f(x) = x² is not one-to-one (it takes both positive and negative values of x to give the same y), we need to restrict the domain to make it invertible. The common restriction is to consider only x ≥ 0.
4. **Final inverse function**: Thus, the inverse function is:
f-1(x) = √x, for x ≥ 0.
In conclusion, the inverse of the function f(x) = x² is f-1(x) = √x, restricted to non-negative values.