Question

PLEASE ANSWER ASAP *picture attached*

Answer 1

1. (rs)(4)=8

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

Explanation:

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

`(rs)(x)=r(x)*s(x)\\\\(rs)(x)=2√(x) *√(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)

`(r)/(s) (x)=(r(x))/(s(x)) \\(r)/(s) (x)=(2√(x) )/(√(x) ) \\(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

`(rs)(4)=8`

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

Explanation:

We have been given two functions
`r(x)=2√(x)` and
`s(x)=√(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√(4)`

`r(4)=2*2`

`r(4)=4`

`s(x)=√(x)`

`s(4)=√(4)`

`s(4)=2`

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

`(rs)(4)=8`

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

To find
`((r)/(s))(3)` we will use rule
`((f)/(g))(x)=(f(x))/(g(x))`.

`((r)/(s))(3)=(r(3))/(s(3))`

`((r)/(s))(3)=(2√(3))/(√(3))`

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

Therefore,
`((r)/(s))(3)=2`.