Question

PLEASE ANSWER ASAP *picture attached*

Answer 1

Answer:

1. (rs)(4)=8

2. (r/s)(3)=2

Step-by-step explanation:

1. To find (r s)(4) we need to find (r s)(x)

$(rs)(x)=r(x)*s(x)\\\\(rs)(x)=2\sqrt{x} *\sqrt{x} \\\\(rs)(x)=2x$

Now we can plug in 4 for x

$(rs)(x)=2x\\(rs)(4)=2(4)\\(rs)(4)=8$

2. To find (r/s)(3) we need to find (r/s)(x), and we can do that by dividing r(x) by s(x)

$\frac{r}{s} (x)=\frac{r(x)}{s(x)} \\\frac{r}{s} (x)=\frac{2\sqrt{x} }{\sqrt{x} } \\\frac{r}{s} (x)=2$

Since (r/s)(x)=2, the output will be always be 2, regardless of what the x value is.  So (r/s)(3)=2

Answer 2

Answer:

$(rs)(4)=8$

$(\frac{r}{s})(3)=2$

Step-by-step explanation:

We have been given two functions $r(x)=2\sqrt{x}$ and $s(x)=\sqrt{x}$.

To find $(rs)(4)$ we will use rule $(f\cdot g)(x)=f(x)\cdot g(x)$.

$(rs)(4)=r(4)\cdot s(4)$

$r(4)=2\sqrt{4}$

$r(4)=2*2$

$r(4)=4$

$s(x)=\sqrt{x}$

$s(4)=\sqrt{4}$

$s(4)=2$

$(rs)(4)=4\cdot 2$

$(rs)(4)=8$

Therefore, $(rs)(4)=8$.

To find $(\frac{r}{s})(3)$ we will use rule $(\frac{f}{g})(x)=\frac{f(x)}{g(x)}$.

$(\frac{r}{s})(3)=\frac{r(3)}{s(3)}$

$(\frac{r}{s})(3)=\frac{2\sqrt{3}}{\sqrt{3}}$

$(\frac{r}{s})(3)=2$

Therefore, $(\frac{r}{s})(3)=2$.