Question

Q(x) = -x + 2r(x) = 4x + 3the following.(q.r)(-4) = (r.a) (-4) =

Answer 1

`\begin{gathered} q(x)=-x+2 \\ r(x)=4x+3 \end{gathered}`

Function composition:

`\begin{gathered} (q\circ r)(x)=q(r(x)) \\ (r\circ q)(x)=r(q(x)) \end{gathered}`

To find the given:

`(q\circ r)(-4)=`

1. Substitute in the equation of function q(x) the x by the equation of function r(x):

`(q\circ r)(x)=-(4x+3)+2`

2. Simplify:

`\begin{gathered} (q\circ r)(x)=-4x-3+2 \\ (q\circ r)(x)=-4x-1 \end{gathered}`

3. Evaluate the equation you get in step 2 when x= -4:

`\begin{gathered} (q\circ r)(-4)=-4(-4)-1 \\ (q\circ r)(-4)=16-1 \\ \\ (q\circ r)(-4)=15 \end{gathered}`

_____________________________--

`(r\circ q)(-4)=`

1.

`(r\circ q)(x)=4(-x+2)+3`

2.

`\begin{gathered} (r\circ q)(x)=-4x+8+3 \\ (r\circ q)(x)=-4x+11 \end{gathered}`

3.

`\begin{gathered} (r\circ q)(-4)=-4(-4)+11 \\ (r\circ q)(-4)=16+11 \\ \\ (r\circ q)(-4)=27 \end{gathered}`

Answe:

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