Final answer:
To find the inverse function of f(x) = x² - 14x + 49 for x ≥ 7, switch the x and y variables, solve for y, and rewrite the equation in terms of y. The inverse function is f⁻¹(x) = 7 ± √x.
Step-by-step explanation:
The question asks for the inverse function of f(x) = x² - 14x + 49 for x ≥ 7.
To find the inverse function, we need to swap the x and y variables and solve for y.
Let's start by rewriting the original function as:
f(x) = x(x - 14) + 49
Now, let's switch the x and y variables:
x = y(y - 14) + 49
To solve for y, we can rearrange the equation:
y² - 14y = x - 49
Completing the square will help us solve for y:
y² - 14y + 49 = x - 49 + 49
(y - 7)² = x
Taking the square root of both sides:
y - 7 = ±√x
y = 7 ± √x
So, the inverse function of f(x) is f⁻¹(x) = 7 ± √x.