Question

F(x) = square root 32x g(x) = square root 2x

Answer 1

Given:

The two functions are:

$f(x)=\sqrt{32x}$

$g(x)=\sqrt{2x}$

To find:

The $(f\cdot g)(x)$. Assume $x\geq 0$.

Solution:

We have,

$f(x)=\sqrt{32x}$

$g(x)=\sqrt{2x}$

Now,

$(f\cdot g)(x)=f(x)\cdot g(x)$

$(f\cdot g)(x)=\sqrt{32x}\cdot \sqrt{2x}$

$(f\cdot g)(x)=\sqrt{32x\times 2x}$

$(f\cdot g)(x)=\sqrt{64x^2}$

$(f\cdot g)(x)=8x$

Therefore, the correct option is A.