To find the inverse of the function f(x) = x² + 25, we need to follow a few steps.
1. Start by replacing f(x) with y:
y = x² + 25
2. Next, swap x and y:
x = y² + 25
3. Now, solve for y. Start by isolating y²:
y² = x – 25
4. Finally, take the square root of both sides to solve for y:
y = √(x – 25)
This means the inverse function is f-1(x) = √(x – 25), valid for x ≥ 25 since the original function only outputs values greater than or equal to 25.