Question

Consider the following function: f(x) = x² - x / (x² - 1) if x ≠ 1, 1 if x = 1. Given that a = 1, what is the value of f(a)?

1) 0
2) 1
3) 2
4) Cannot be determined

Answer 1

The function f(x) is given as 1 if x = 1, so for a = 1, the value of f(a) is directly given as 1.

Step-by-step explanation:

The value of the function f(x) at x = 1 is explicitly given as f(1) = 1. Therefore, when we substitute a = 1 into the function, f(a) = f(1) = 1, irrespective of the expression defined for values of x that are not equal to 1. According to the given function, the value does not need to be determined through calculation for cases where x equals 1, as the function defines it clearly. Hence, for this piecewise function, the answer for f(a) when a is 1, is simply 1.