Answer:
78
Step-by-step explanation:
Multiply f(x) and g(x) then evaluate for x = - 5
f(x) × g(x)
= (- 2x - 7)(- 4x + 6) ← substitute x = - 5 into the expression
= (10 - 7)(20 + 6)
= 3 × 26
= 78
For this case we have the following functions:
[tex]f (x) = - 2x-7\\g (x) = - 4x + 6[/tex]
We must find [tex](f * g) (x).[/tex] By definition we have to:
[tex](f * g) (x) = f (x) * g (x)[/tex]
So:
[tex](f * g) (x) = (- 2x-7) (- 4x + 6)[/tex]
We apply distributive property keeping in mind that:
[tex]- * - = +\\- * + = -\\(f * g) (x) = 8x ^ 2-12x + 28x-42\\(f * g) (x) = 8x ^ 2 + 16x-42[/tex]
We evaluate in [tex]x = -5[/tex]:
[tex](f * g) (- 5) = 8 (-5) ^ 2 + 16 (-5) -42\\(f * g) (- 5) = 8 * 25-80-42\\(f * g) (- 5) = 200-80-42\\(f * g) (- 5) = 78[/tex]
Answer:
[tex](f * g) (- 5) = 78[/tex]
