Question

Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (fxg)(-5).

Answer 1

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

Answer 2

For this case we have the following functions:

$f (x) = - 2x-7\\g (x) = - 4x + 6$

We must find $(f * g) (x).$ By definition we have to:

$(f * g) (x) = f (x) * g (x)$

So:

$(f * g) (x) = (- 2x-7) (- 4x + 6)$

We apply distributive property keeping in mind that:

$- * - = +\\- * + = -\\(f * g) (x) = 8x ^ 2-12x + 28x-42\\(f * g) (x) = 8x ^ 2 + 16x-42$

We evaluate in $x = -5$:

$(f * g) (- 5) = 8 (-5) ^ 2 + 16 (-5) -42\\(f * g) (- 5) = 8 * 25-80-42\\(f * g) (- 5) = 200-80-42\\(f * g) (- 5) = 78$

Answer:

$(f * g) (- 5) = 78$