Question

What is the inverse of the function f(x)=3(x+4)²-2, sucts that x<=-4 ?

Answer 1

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