Final answer:
To solve the inequality g(x) > 0 for the function g(x)=(x-1)/(x+1), we need to find the values of x that make the function greater than 0. The solution to the inequality g(x) > 0 is x ∈ (-1, 1).
Step-by-step explanation:
To solve the inequality g(x) > 0 for the function g(x)=(x-1)/(x+1), we need to find the values of x that make the function greater than 0. We can start by finding the critical points, which are the values of x that make the function equal to 0 or undefined. To make the function equal to 0, we set the numerator (x-1) equal to 0, which gives x = 1. This is a critical point. To make the function undefined, we set the denominator (x+1) equal to 0, which gives x = -1. This is another critical point. Next, we create a number line and test intervals between these critical points. For values of x less than -1, the function is negative. For values of x between -1 and 1, the function is positive. For values of x greater than 1, the function is negative. Therefore, the solution to the inequality g(x) > 0 is x ∈ (-1, 1).