Final answer:
To find the inverse of the function f(x) = 3(x + 4)² - 2, we need to interchange x and y and solve for y. The inverse function is given by f^(-1)(x) = √[(x + 2)/3] - 4.
Step-by-step explanation:
To find the inverse of the function f(x) = 3(x + 4)² - 2, we need to interchange x and y and solve for y. Let's start by interchanging x and y:
x = 3(y + 4)² - 2
Now, let's isolate y:
x + 2 = 3(y + 4)²
Divide both sides by 3:
(x + 2)/3 = (y + 4)²
Take the square root of both sides:
√[(x + 2)/3] = y + 4
Subtract 4 from both sides:
√[(x + 2)/3] - 4 = y
Now we have the inverse function:
f^(-1)(x) = √[(x + 2)/3] - 4