Question

Which function defines the inverse of the rational function f(x)=(-1)/(x+1) for x!=-1 ?

Answer 1

The inverse of the rational function f(x) = -1 / (x+1) is f^(-1)(x) = 1/x - 1.

Step-by-step explanation:

The process of finding the inverse of a rational function involves swapping the roles of x and y and solving for y. In this case, the given rational function is f(x) = -1 / (x+1). To find its inverse, follow these steps:

1. Replace f(x) with y: y = -1 / (x+1)
2. Swap x and y: x = -1 / (y+1)
3. Solve for y: Multiply both sides by (y+1) and isolate y by subtracting 1 from both sides. This gives -x(y+1) = -1. Simplify to y+1 = 1/x. Subtract 1 from both sides: y = 1/x - 1

Therefore, the inverse of the given rational function is f^(-1)(x) = 1/x - 1.