Question

What is the inverse of g(x)=1/x-1
and is it a function?

Answer 1

The inverse of the function g(x) = 1/(x-1) is g^-1(x) = (1 + x)/x. The inverse function is a function if each x-value has a unique corresponding y-value.

Step-by-step explanation:

The inverse of the function g(x) = 1/(x-1) can be found by swapping the x and y variables and solving for y. Let's start with the original function:

g(x) = 1/(x-1)

Swap x and y:

x = 1/(y-1)

Now solve for y:

x(y-1) = 1

xy - x = 1

xy = 1 + x

y = (1 + x)/x

So, the inverse function is g-1(x) = (1 + x)/x. It is important to note that the inverse of a function is only a function if every value of x has a corresponding unique value of y, meaning that no two x-values can have the same y-value. In this case, the inverse function is indeed a function.