Question

If $f\left(x\right)=x^3$ and $g\left(x\right)=sin2x$, then

• A. $g\left[f\right(1\left)\right]=1$
• B. $f\left(g\right(\pi /12)=1/8$
• C. $gf\left(2\right)=\sin 2$
• D. none of these

Answer 1

Answer: (B)

$f\left(g\right(\pi /12)=1/8$

Given,
$f\left(x\right)=x^3$ and $g\left(x\right)=\sin 2x$

Clearly,

$f\left(1\right)=1\Rightarrow g\left[f\right(1\left)\right]=\sin 2$

$g\left(\frac{\pi }{12}\right)=\frac{1}{2}\Rightarrow f\left[g\right(\frac{\pi }{12}\left)\right]=\frac{1}{8}$

and,$f\left(2\right)=8\Rightarrow g\left[f\right(2\left)\right]=\sin 16$

So, the correct option is (B).