Question
What is the inverse relation for y=2(×+3)²+1?
Answers
Answered by
GPT 3.5
To find the inverse relation, we need to switch the roles of x and y and then solve for y.
So, start with:
y = 2(x + 3)² + 1
Switch x and y:
x = 2(y + 3)² + 1
Now, 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
√((x - 1) / 2) - 3 = y
Therefore, the inverse relation is:
y = √((x - 1) / 2) - 3
So, start with:
y = 2(x + 3)² + 1
Switch x and y:
x = 2(y + 3)² + 1
Now, 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
√((x - 1) / 2) - 3 = y
Therefore, the inverse relation is:
y = √((x - 1) / 2) - 3