Answer: x = -6 ±√(y + 36)
Explanation: To find the inverse of the function y = x^2 + 12x, we first need to express x in terms of y, and then interchange the roles of x and y.
So, starting with the given equation:
y = x^2 + 12x
We can complete the square by adding and subtracting 36, which is (12/2)^2, inside the parentheses on the right-hand side:
y = x^2 + 12x + 36 - 36
This allows us to rewrite the right-hand side as a perfect square trinomial:
y = (x + 6)^2 - 36
Now, we can solve for x in terms of y by adding 36 to both sides and taking the square root:
x + 6 = ±√(y + 36)
x = -6 ±√(y + 36)
Finally, we interchange the roles of x and y to obtain the inverse function:
y = -6 ±√(x + 36)
Therefore, the inverse of y = x^2 + 12x is:
x = -6 ±√(y + 36)