5. determine the period of the function: g(x) = cos(4(x - π)) a) π b) 2π c) 4π d) π/2

Explanation:

Step1: Recall cosine - function period formula

The general form of a cosine function is $y = A\cos(B(x - C))+D$, and its period $T$ is given by $T=\frac{2\pi}{|B|}$.

Step2: Identify the value of B

For the function $g(x)=\cos(4(x - \pi))$, we have $B = 4$.

Step3: Calculate the period

Substitute $B = 4$ into the period formula $T=\frac{2\pi}{|B|}$, so $T=\frac{2\pi}{4}=\frac{\pi}{2}$.

Answer:

D. $\frac{\pi}{2}$