Question

For the given graph of $f\left(x\right)=\cos x.$ Select the correct statements.

• A. $g\left(x\right)=2\cos x$
• B. $h\left(x\right)=0.25\cos x$
• C. $h\left(x\right)=0.5+\cos x$
• D. $g(x{)}_{max}=4\times h(x{)}_{max}$

Answer 1

Answer: (A), (D)

$g(x{)}_{max}=4\times h(x{)}_{max}$

Given the graph of the functions as:

Here, $f\left(x\right)=\cos x$ and $h\left(x\right)$ is a function shrunk $0.5$ times the function $f\left(x\right)$
$\Rightarrow h\left(x\right)=0.5\cos x$
Similarly, $g\left(x\right)$ is a function stretched $2$ times the function $f\left(x\right)$
$\Rightarrow g\left(x\right)=2\cos x$

Also, $h(x{)}_{max}=0.5$ and $g(x{)}_{max}=2$
$\Rightarrow g(x{)}_{max}=4\times h(x{)}_{max}$