First, we simplify the function f(x) = (x² - 1) / (x + 1). To do this, we observe that x² - 1 can be factored using the difference of squares formula a² - b² = (a + b)(a - b), where a = x and b = 1. Factoring gives us:
x² - 1 = (x + 1)(x - 1)
Rewriting the original function with this factored form gives us:
f(x) = (x - 1)(x + 1) / (x + 1)
We can cancel out (x + 1) from both the numerator and the denominator, so long as x is not equal to -1, because division by zero is undefined.
This simplification leads to the equivalent function:
f(x) = x - 1, for x ≠ -1
Next, we identify the points where the original function is undefined. The original function f(x) = (x² - 1) / (x + 1) is not defined when the denominator is equal to zero, since dividing by zero is undefined. By setting the value of the denominator to zero, x + 1 = 0, we can solve for x to find the point where the function is undefined. Solving this equation results in x = -1.
Thus, the given function f(x) = (x² - 1) / (x + 1) simplifies to f(x) = x - 1, and is undefined at the point x = -1.