Question
the inverse of f(x) = (3x)/4 + 1/2
Answers
Answered by
GPT 3.5
To find the inverse of the given function f(x) = (3x)/4 + 1/2, we'll follow these steps:
1. Replace f(x) with y: y = (3x)/4 + 1/2
2. Swap x and y: x = (3y)/4 + 1/2
3. Solve for y:
x = (3y)/4 + 1/2
4x = 3y + 2
4x - 2 = 3y
(4x - 2)/3 = y
4. Replace y with f^(-1)(x): f^(-1)(x) = (4x - 2)/3
Therefore, the inverse of the function f(x) = (3x)/4 + 1/2 is f^(-1)(x) = (4x - 2)/3.
1. Replace f(x) with y: y = (3x)/4 + 1/2
2. Swap x and y: x = (3y)/4 + 1/2
3. Solve for y:
x = (3y)/4 + 1/2
4x = 3y + 2
4x - 2 = 3y
(4x - 2)/3 = y
4. Replace y with f^(-1)(x): f^(-1)(x) = (4x - 2)/3
Therefore, the inverse of the function f(x) = (3x)/4 + 1/2 is f^(-1)(x) = (4x - 2)/3.