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Suppose that the functions q and r are defined as follows.
q (x) = 2x+2
r(x) = x² +1
Find the following.
(r •q)(-3) = 0

(q •r)(-3) = 0

Suppose that the functions q and r are defined as follows q x 2x2 rx x 1 Find the following r q3 0 q r3 0 class=

Respuesta :

Given:

The two functions are [tex]q(x)=2x+2[/tex], [tex]r(x)=x^2+1[/tex]

We need to determine the value of [tex](r \circ q)(-3)[/tex] and [tex](q \circ r)(-3)[/tex]

Value of [tex](r \circ q)(-3)[/tex]:

Let us determine the value of  [tex](r \circ q)(-3)[/tex]

[tex](r \circ q)(x)=r[q(x)][/tex]

              [tex]=r(2x+2)[/tex]

              [tex]=(2x+2)^2+1[/tex]

              [tex]=4x^2+8x+5[/tex]

Now, substituting x = -3, we get;

[tex](r \circ q)(-3)=4(-3)^2+8(-3)+5[/tex]

                 [tex]=4(9)-24+5[/tex]

                 [tex]=36-24+5[/tex]

[tex](r \circ q)(-3)=17[/tex]

Thus, the value of [tex](r \circ q)(-3)[/tex] is 17

Value of [tex](q \circ r)(-3)[/tex]:

Let us determine the value of [tex](q \circ r)(x)[/tex]

[tex](q \circ r)(x)=q[r(x)][/tex]

              [tex]=q(x^2+1)[/tex]

              [tex]=2(x^2+1)+2[/tex]

             [tex]=2x^2+2+2[/tex]

[tex](q \circ r)(x)=2x^2+4[/tex]

Substituting x = -3, we get;

[tex](q \circ r)(-3)=2(-3)^2+4[/tex]

                 [tex]=2(9)+4[/tex]

[tex](q \circ r)(-3)=22[/tex]

Thus, the value of [tex](q \circ r)(x)[/tex] is 22.

abidemiokin

The function (r •q)(-3) =(q •r)(-3)  and they are equal to -40

Given the following functions

q(x) = 2x+2

r(x) = x² +1

Taking the product

q(x)*r(x) = (2x+2)(x² +1)

Note that according to the communatative law, (r •q)(x) = (q •r)(x)

(r •q)(-3) =(q •r)(-3) = (2(-3)+2)((-3)² +1)

(r •q)(-3) =(q •r)(-3) = (-4)(9+1)

(r •q)(-3) =(q •r)(-3) = -4(10)

(r •q)(-3) =(q •r)(-3) =-40

Hence the function (r •q)(-3) =(q •r)(-3)  and they are equal to -40

Learn more here: https://brainly.com/question/4854699

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