Question

Find the inverse function of f
F(x)=x/x+3
Then f inverse (x) is

Answer 1

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

Starting with F(x) = x/(x+3):

1. Swap x and y: x = y/(y+3)
2. Solve for y: xy + 3x = y
3. Move all terms to one side: xy - y = -3x
4. Factor out y: y(x - 1) = -3x
5. Divide both sides by (x - 1): y = -3x / (x - 1)

Therefore, the inverse of f(x) = x/(x+3) is given by f^(-1)(x) = -3x / (x - 1).