Question

Given below the graph of $y=\cos 4x;x\in R.$
Select the correct statements for the given function.

• A. Range: $[-1,1]$
• B. Period: $2\pi$
• C. Range: $[-4,4]$
• D. Period: $\frac{\pi }{2}$

Answer 1

Answer: (A), (D)

Period: $\frac{\pi }{2}$

Given the graph of:
$y=\cos 4x;x\in R$


As observed from the graph, the function ranges from $-1\text{to}1$
$\text{Or}y\in [-1,1]$
That means range of $\cos 4x:[-1,1]$

Now, using the fact that if $f\left(x\right)$ has a period $T.$
Then, $f(ax+b)$ will have a period $\frac{T}{|a|}.$

Using the same concept. we know $\cos x$ has a fundamental period $2\pi$
$\Rightarrow \cos 4x$ will have a fundamental period $\frac{2\pi }{4}\text{or}\frac{\pi }{2}$
Hence, $\cos 4x$ has a period $\frac{\pi }{2}.$