[tex]\begin{gathered} q(x)=-x+2 \\ r(x)=4x+3 \end{gathered}[/tex]
Function composition:
[tex]\begin{gathered} (q\circ r)(x)=q(r(x)) \\ (r\circ q)(x)=r(q(x)) \end{gathered}[/tex]
To find the given:
[tex](q\circ r)(-4)=[/tex]
1. Substitute in the equation of function q(x) the x by the equation of function r(x):
[tex](q\circ r)(x)=-(4x+3)+2[/tex]
2. Simplify:
[tex]\begin{gathered} (q\circ r)(x)=-4x-3+2 \\ (q\circ r)(x)=-4x-1 \end{gathered}[/tex]
3. Evaluate the equation you get in step 2 when x= -4:
[tex]\begin{gathered} (q\circ r)(-4)=-4(-4)-1 \\ (q\circ r)(-4)=16-1 \\ \\ (q\circ r)(-4)=15 \end{gathered}[/tex]
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[tex](r\circ q)(-4)=[/tex]
1.
[tex](r\circ q)(x)=4(-x+2)+3[/tex]
2.
[tex]\begin{gathered} (r\circ q)(x)=-4x+8+3 \\ (r\circ q)(x)=-4x+11 \end{gathered}[/tex]
3.
[tex]\begin{gathered} (r\circ q)(-4)=-4(-4)+11 \\ (r\circ q)(-4)=16+11 \\ \\ (r\circ q)(-4)=27 \end{gathered}[/tex]
Answe:
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