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Answer :
To find (f • g)(x), substitute g(x) into f(x) and simplify. The resulting expression is [tex]-40x^2 + 25x + 45[/tex]. The correct choice is option B.
To find (f • g)(x), we need to compute f(g(x)).
This means we will substitute g(x) into f(x).
Start with g(x): g(x) = [tex]8x^2 - 5x - 9[/tex]
Substitute g(x) into f(x): f(g(x)) = [tex]-5 * (8x^2 - 5x - 9)[/tex]
Distribute -5 through the expression: f(g(x)) = [tex]-5 * 8x^2 + (-5) * (-5x) + (-5) * (-9)[/tex]
Perform the multiplication: f(g(x)) = [tex]-40x^2 + 25x + 45[/tex]
So, (f • g)(x) = [tex]-40x^2 + 25x + 45[/tex].
The correct answer is option B: [tex]-40x^2 + 25x + 45[/tex].
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