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Suppose that the functions [tex] q [/tex] and [tex] r [/tex] are defined as follows.

[tex]
\begin{array}{l}
q(x) = 5x \\
r(x) = 4x + 4
\end{array}
[/tex]

Find the following:

[tex]
\begin{array}{l}
(q \circ r)(-2) = \\
(r \circ q)(-2) =
\end{array}
[/tex]

Sagot :

GinnyAnsweridn
Let's find [tex]\((q \circ r)(-2)\)[/tex] and [tex]\((r \circ q)(-2)\)[/tex] using the definitions of the functions [tex]\(q(x) = 5x\)[/tex] and [tex]\(r(x) = 4x + 4\)[/tex].

### Finding [tex]\((q \circ r)(-2)\)[/tex]
The composition [tex]\( (q \circ r)(x) \)[/tex] means we first apply the function [tex]\( r \)[/tex] to [tex]\( x \)[/tex], and then apply the function [tex]\( q \)[/tex] to the result of [tex]\( r(x) \)[/tex].

1. Calculate [tex]\( r(-2) \)[/tex]:
[tex]\[ r(-2) = 4(-2) + 4 = -8 + 4 = -4 \][/tex]

2. Apply [tex]\( q \)[/tex] to the result of [tex]\( r(-2) \)[/tex]:
[tex]\[ q(r(-2)) = q(-4) = 5(-4) = -20 \][/tex]

So, [tex]\((q \circ r)(-2) = -20\)[/tex].

### Finding [tex]\((r \circ q)(-2)\)[/tex]
The composition [tex]\( (r \circ q)(x) \)[/tex] means we first apply the function [tex]\( q \)[/tex] to [tex]\( x \)[/tex], and then apply the function [tex]\( r \)[/tex] to the result of [tex]\( q(x) \)[/tex].

1. Calculate [tex]\( q(-2) \)[/tex]:
[tex]\[ q(-2) = 5(-2) = -10 \][/tex]

2. Apply [tex]\( r \)[/tex] to the result of [tex]\( q(-2) \)[/tex]:
[tex]\[ r(q(-2)) = r(-10) = 4(-10) + 4 = -40 + 4 = -36 \][/tex]

So, [tex]\((r \circ q)(-2) = -36\)[/tex].

### Conclusion
[tex]\[ (q \circ r)(-2) = -20 \][/tex]
[tex]\[ (r \circ q)(-2) = -36 \][/tex]
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