Final answer:
The restriction on the domain of the function f(x) = (x - 1)/(x + 4) is where the denominator equals zero, which is at x = -4. Therefore, the function is undefined at x = -4, making the correct answer A: x ≠ -4.
Step-by-step explanation:
To identify the restrictions on the domain of the function f(x) = (x - 1)/(x + 4), we need to consider the values of x for which the function is not defined. The function given is a rational function, and rational functions are undefined where the denominator is equal to zero.
In the function f(x) = (x - 1)/(x + 4), the denominator is x + 4. The restriction on the domain occurs where the denominator is zero because division by zero is undefined in mathematics. Therefore, we set the denominator equal to zero and solve for x: x + 4 = 0, which gives x = -4.
Hence, the only restriction on the domain of the function is when x ≠ -4, since that would make the denominator zero and the function undefined.
The correct answer is A: x ≠ -4.