Find the inverse of.....
f(x)=(4x-1)/(2x+3)
Is the inverse this:
f^-1(x)= (1/2)((-3x-1)/(x-2))
correct
To find the inverse of a function, we typically follow these steps:
1. Replace f(x) with y: y = (4x - 1)/(2x + 3).
2. Swap the x and y variables: x = (4y - 1)/(2y + 3).
3. Solve the equation for y.
- Start by multiplying both sides of the equation by (2y + 3) to eliminate the denominator: x(2y + 3) = 4y - 1.
- Distribute x on the left side: 2xy + 3x = 4y - 1.
- Move all terms containing y to one side: 2xy - 4y = -3x - 1.
- Factor out y on the left side: y(2x - 4) = -3x - 1.
- Divide both sides by (2x - 4): y = (-3x - 1)/(2x - 4).
4. Replace y with f^(-1)(x): f^(-1)(x) = (-3x - 1)/(2x - 4).
So, the inverse of the function f(x) = (4x - 1)/(2x + 3) is:
f^(-1)(x) = (-3x - 1)/(2x - 4)