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)

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Arshadul0036 Arshadul0036

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Mathematics

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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 :

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bayosanuade bayosanuade · Answer 1 · 2025-03-25T22:45:22-04:00

Answer:

Step-by-step explanation:

Given:

[tex]f(x) = 2 - 3x[/tex]

[tex]g(x) = -x - 1[/tex]

1. [tex](f-g) =[/tex] [tex]2 - 3x - ( -x - 1 )[/tex]

[tex](f-g) = 2 - 3x + x + 1[/tex]

[tex](f-g) = 3 - 2x[/tex]

therefore : [tex](f-g) (-3)[/tex] means that we are substituting - 3 for x , that is

[tex](f-g)(-3) =[/tex] [tex]3 - 2 ( - 3 )[/tex]

[tex](f-g)(-3) =[/tex] [tex]3+6[/tex]

[tex](f-g)(-3) =[/tex] [tex]9[/tex]

2. [tex](f-g)(x) = 3 - 2x[/tex]

3. ([tex]f[/tex] x [tex]g )[/tex] = [tex](2-3x)(-x-1)[/tex]

([tex]f[/tex] x [tex]g )[/tex] = [tex]2(-x-1) -3x(-x-1)[/tex]

([tex]f[/tex] x [tex]g )[/tex] = [tex]-2x - 2[/tex] [tex]+ 3x^{2}+3x[/tex]

([tex]f[/tex] x [tex]g )[/tex] = [tex]3x^{2}+x - 2[/tex]

Therefore :

([tex]f[/tex] x [tex]g )[/tex][tex](-1)[/tex] = [tex]3(-1)^{2}[/tex] [tex]+(-1) - 2[/tex]

([tex]f[/tex] x [tex]g )[/tex][tex](-1) =[/tex] [tex]3 - 1 - 2[/tex]

([tex]f[/tex] x [tex]g )[/tex][tex](-1) =0[/tex]

4. ([tex]f[/tex] x [tex]g )[/tex](x) = [tex]3x^{2}+x - 2[/tex]

5. [tex]f(x-1)[/tex] , this means that we will substitute [tex]x-1[/tex] for [tex]x[/tex] in [tex]f(x)[/tex] , that is

[tex]f(x-1)[/tex] = [tex]2 - 3(x-1)[/tex]

[tex]f(x-1)[/tex] = [tex]2 - 3x + 3[/tex]

[tex]f(x-1)[/tex] = [tex]5 - 3x[/tex]

6. [tex]f(x-1)[/tex][tex]-f(1)[/tex] = [tex]5 - 3x[/tex] [tex]- (2-3(1) )[/tex]

[tex]f(x-1) - f(1)[/tex] = [tex]5 - 3x +1[/tex]

[tex]f(x-1) - f(1)[/tex] = [tex]6 - 3x[/tex]

7. [tex]g(x+2)- g(2)[/tex]

[tex]g(x+2) = -(x+2) - 1[/tex]

[tex]g(x+2) =[/tex] [tex]-x-2-1[/tex]

[tex]g(x+2) =[/tex] [tex]-x - 3[/tex]

[tex]g(2) = -2-1 = -3[/tex]

Therefore :

[tex]g(x+2)- g(2)[/tex] = [tex]-x - 3 -(- 3)[/tex]

[tex]g(x+2)- g(2)[/tex] = [tex]-x[/tex]

8. [tex]g(x+h) - g (x)[/tex]

[tex]g(x+h) = -(x+h) - 1 = -x - h - 1[/tex]

Therefore :

[tex]g(x+h) - g (x)[/tex] = [tex]-x - h - 1[/tex] - [tex](-x-1)[/tex]

[tex]g(x+h) - g (x)[/tex] = [tex]-x - h - 1 + x + 1[/tex]

[tex]g(x+h) - g (x)[/tex] = [tex]-h[/tex]

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 :

Other Questions

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)