what is the period of the function g(x)=2 cos(7x + 5)+1? give an exact value. units

Explanation:

Step1: Recall cosine - function period formula

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

Step2: Identify the value of B in the given function

For the function $g(x)=2\cos(7x + 5)+1$, comparing with the general form, we have $B = 7$.

Step3: Calculate the period

Substitute $B = 7$ into the period formula $T=\frac{2\pi}{|B|}$. Since $|7| = 7$, we get $T=\frac{2\pi}{7}$.

Answer:

$\frac{2\pi}{7}$