Given:
The two functions are:
[tex]f(x)=\sqrt{32x}[/tex]
[tex]g(x)=\sqrt{2x}[/tex]
To find:
The [tex](f\cdot g)(x)[/tex]. Assume [tex]x\geq 0[/tex].
Solution:
We have,
[tex]f(x)=\sqrt{32x}[/tex]
[tex]g(x)=\sqrt{2x}[/tex]
Now,
[tex](f\cdot g)(x)=f(x)\cdot g(x)[/tex]
[tex](f\cdot g)(x)=\sqrt{32x}\cdot \sqrt{2x}[/tex]
[tex](f\cdot g)(x)=\sqrt{32x\times 2x}[/tex]
[tex](f\cdot g)(x)=\sqrt{64x^2}[/tex]
[tex](f\cdot g)(x)=8x[/tex]
Therefore, the correct option is A.
