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Given the functions [tex]\( a \)[/tex] and [tex]\( b \)[/tex] below, find [tex]\( a(b(5)) \)[/tex].

[tex]\[
\begin{array}{l}
a(x) = -x^2 + 7x + 1 \\
b(x) = 3x - 5
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To find [tex]\( a(b(5)) \)[/tex], we need to follow a step-by-step approach. Let's break it down:

1. Evaluate [tex]\( b(5) \)[/tex]:
We start by substituting [tex]\( x = 5 \)[/tex] into the function [tex]\( b(x) \)[/tex].
[tex]\[ b(x) = 3x - 5 \][/tex]
So,
[tex]\[ b(5) = 3 \cdot 5 - 5 = 15 - 5 = 10 \][/tex]

2. Use the result of [tex]\( b(5) \)[/tex] to evaluate [tex]\( a(b(5)) \)[/tex]:
We have found that [tex]\( b(5) = 10 \)[/tex]. Now we need to substitute [tex]\( x = 10 \)[/tex] into the function [tex]\( a(x) \)[/tex].
[tex]\[ a(x) = -x^2 + 7x + 1 \][/tex]
So,
[tex]\[ a(10) = -(10)^2 + 7 \cdot 10 + 1 \][/tex]
Simplifying inside the function:
[tex]\[ a(10) = -100 + 70 + 1 = -100 + 71 = -29 \][/tex]

Hence, the final result is:
[tex]\[ a(b(5)) = -29 \][/tex]

So, [tex]\( b(5) = 10 \)[/tex] and [tex]\( a(b(5)) = -29 \)[/tex].
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