Question

I need help with several math problems it says given f(x)=2-3x and g (x) = -x-1 Find the following and Simplify when possible. 1. (f-g) (-3) 2. (f-g) (x) 3. (f × g) (-1) d. (f ×g) (x) E. f (x-1) F. f (x-1)-f (1) G. g(x+2)-g (2) h. g (x+h) - g(x) ​

Answer 1

Explanation:

Given:

`f(x) = 2 - 3x`

`g(x) = -x - 1`

1.
`(f-g) =`
`2 - 3x - ( -x - 1 )`

`(f-g) = 2 - 3x + x + 1`

`(f-g) = 3 - 2x`

therefore :
`(f-g) (-3)` means that we are substituting - 3 for x , that is

`(f-g)(-3) =`
`3 - 2 ( - 3 )`

`(f-g)(-3) =`
`3+6`

`(f-g)(-3) =`
`9`

2.
`(f-g)(x) = 3 - 2x`

3. (
`f` x
`g )` =
`(2-3x)(-x-1)`

(
`f` x
`g )` =
`2(-x-1) -3x(-x-1)`

(
`f` x
`g )` =
`-2x - 2`
`+ 3x^(2)+3x`

(
`f` x
`g )` =
`3x^(2)+x - 2`

Therefore :

(
`f` x
`g )`
`(-1)` =
`3(-1)^(2)`
`+(-1) - 2`

(
`f` x
`g )`
`(-1) =`
`3 - 1 - 2`

(
`f` x
`g )`
`(-1) =0`

4. (
`f` x
`g )`(x) =
`3x^(2)+x - 2`

5.
`f(x-1)` , this means that we will substitute
`x-1` for
`x` in
`f(x)` , that is

`f(x-1)` =
`2 - 3(x-1)`

`f(x-1)` =
`2 - 3x + 3`

`f(x-1)` =
`5 - 3x`

6.
`f(x-1)`
`-f(1)` =
`5 - 3x`
`- (2-3(1) )`

`f(x-1) - f(1)` =
`5 - 3x +1`

`f(x-1) - f(1)` =
`6 - 3x`

7.
`g(x+2)- g(2)`

`g(x+2) = -(x+2) - 1`

`g(x+2) =`
`-x-2-1`

`g(x+2) =`
`-x - 3`

`g(2) = -2-1 = -3`

Therefore :

`g(x+2)- g(2)` =
`-x - 3 -(- 3)`

`g(x+2)- g(2)` =
`-x`

8.
`g(x+h) - g (x)`

`g(x+h) = -(x+h) - 1 = -x - h - 1`

Therefore :

`g(x+h) - g (x)` =
`-x - h - 1` -
`(-x-1)`

`g(x+h) - g (x)` =
`-x - h - 1 + x + 1`

`g(x+h) - g (x)` =
`-h`