Question

Pl ease H e l p I'm literally desperate-

If f(x) = 4x - 5 and g(x) = 7x -3, Show all steps & work. Find:
(f + g) (x)
and
(f * g) (x)

Answer 1

Explanation:

Step 1: Find (f + g)(x)

The definition of (f + g)(x) is f(x) + g(x). Basically add the two functions together.

`f(x) + g(x)`

`(4x - 5) + (7x - 3)`

`11x - 8`

Answer:
`11x - 8`

Step 2: Find (f * g)(x)

The definition of (f * g)(x) is f(x) * g(x). Basically multiply the two functions together.

`f(x) * g(x)`

`(4x - 5) * (7x - 3)`

`(4x * 7x) + (4x * -3) + (-5 * 7x) + (-5 * -3)`

`(28x^(2)) + (-12x) + (-35x) + (15)`

`28x^(2) - 47x + 15`

Answer:
`28x^(2) - 47x + 15`

Answer 2

f+g = 11x-8

f*g = 28x^2 - 47x+15

Explanation:

f(x) = 4x - 5 and g(x) = 7x -3

(f+g)(x) = 4x - 5 + 7x -3

Combine like terms

= 4x+7x -5-3

= 11x-8

(f * g) (x) = ( 4x - 5) (7x -3)

FOIL

= 4x*7x + 4x(-3) + (-5)(7x) + (-5)(-3)

=28x^2 -12x-35x+15

Combine like terms

=28x^2 - 47x+15