Question

Let $f\left(x\right)={[3{\sin }^2(10x+11)-7]}^2$ for $x\in R$. Then, the maximum value of the function $f$ is

• A. $9$
• B. $16$
• C. $49$
• D. $100$
• E. $121$

Answer 1

The correct option is A $9$

$f\left(x\right)={[3{\sin }^2(10x+11)-7]}^2$ will have maximum value when ${\sin }^2(10x+11)$ has minimum value.
[$\because {\sin }^2\theta$ is always $+ve$]
Therefore, minimum value of ${\sin }^2(10x+11)=0$
and maximum value of $f\left(x\right)={(-7)}^2=49$