Question

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

Answer 1

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`

Answer 2

78

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