Question

Given the graph of $y=5\cos (2x+1);\forall x\in R.$ Select the correct options.

• A. Range:$[-5,5]$
• B. Period: $\pi$
• C. Range: $[-1,1]$
• D. Period: $4\pi$

Answer 1

Answer: (A), (B)

Period: $\pi$

Given the graph of $y=5\cos (2x+1);\forall x\in R.$


Here, $y$ ranges from $-5\text{to}5$
$\text{or}-5\le y\le 5\Rightarrow 5\cos (2x+1)\in [-5,5]$

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 $2\pi$
$\Rightarrow 5\cos (2x+1)$ will have a fundamental period $\frac{2\pi }{2}\text{or}\pi$
Hence, $5\cos (2x+1)$ has a period $\pi .$