To find and simplify [tex]\((f \cdot g)(4.5)\)[/tex] where [tex]\( f(x) = -x + 3 \)[/tex] and [tex]\( g(x) = -12x - 10 \)[/tex], follow these steps:
1. Evaluate [tex]\( f(x) \)[/tex] at [tex]\( x = 4.5 \)[/tex]:
[tex]\[
f(4.5) = -4.5 + 3 = -1.5
\][/tex]
2. Evaluate [tex]\( g(x) \)[/tex] at [tex]\( x = 4.5 \)[/tex]:
[tex]\[
g(4.5) = -12(4.5) - 10 = -54 - 10 = -64
\][/tex]
3. Now, compute the product [tex]\( (f \cdot g)(4.5) \)[/tex]:
[tex]\[
(f \cdot g)(4.5) = f(4.5) \cdot g(4.5) = -1.5 \cdot -64 = 96
\][/tex]
Therefore, [tex]\((f \cdot g)(4.5)\)[/tex] simplifies to 96.
