Question

The functions q and r are defined as follows.

q(x) = -x - 2
r(x) = -2x^2 -2
Find the value of r(q(-4)) .

Answer 1

For this case we have the following functions:

`q (x) = - x-2\\r (x) = - 2x ^ 2-2`

We must find
`r (q (x))`. So:

We substitute
`q (x)`in
`r (x).`

`r (q (x)) = - 2 (-x-2) ^ 2-2`

Now we substitute
`x = -4`

`r (q (-4)) = - 2 (- (- 4) -2) ^ 2-2\\r (q (-4)) = - 2 (+ 4-2) ^ 2-2\\r (q (-4)) = - 2 (2) ^ 2-2\\r (q (-4)) = - 2 (4) -2\\r (q (-4)) = - 8-2\\r (q (-4)) = - 10`

Answer:

`r (q (-4)) = - 10`

Answer 2

r(q(-4)) = -10

Explanation:

q(x) = -x - 2

r(x) = -2x^2 -2

r(q(-4))

First find q(-4)

Let x=-4

q(-4) = -(-4) - 2

q(-4) = +4 -2 = 2

q(-4) =2

We substitute this value in for x in r(x)

r(2) = -2(2)^2 -2

= -2 (4) -2

= -8 -2

= -10