Question #N953
A function f is defined by \(f(x) = \frac{x^2 - 4}{x + 2}\). For what value of x does f(x) = 4?
A. -6
B. -2
C. 2
D. 6
Correct Answer is: D
To find the value of x for which f(x) = 4, we set \(\frac{x^2 - 4}{x + 2}\) equal to 4 and solve for x: \begin{aligned} \frac{x^2 - 4}{x + 2} &= 4\\ x^2 - 4 &= 4(x + 2)\\ x^2 - 4 &= 4x + 8\\ x^2 - 4x - 12 &= 0\\ (x - 6)(x + 2) &= 0\\ x &= 6, -2 \end{aligned} Since the function is undefined when x = -2, the only solution is x = 6.