Question

What is the inverse of y=2(x+3)²+1

Answer 1

To find the inverse of a function, we need to switch the roles of x and y and solve for y.

So, let's start with the original function:
y = 2(x + 3)² + 1

Switching x and y:
x = 2(y + 3)² + 1

Now, let's solve for y:
x = 2(y + 3)² + 1
x - 1 = 2(y + 3)²
(x - 1)/2 = (y + 3)²
√((x - 1)/2) = y + 3
y = √((x - 1)/2) - 3

Therefore, the inverse of y=2(x+3)²+1 is y = √((x - 1)/2) - 3.