a.) f+g

b.) f-g

c.) f⋅g

d.) f/g

e.) g/f

a.) f+g

b.) f-g

c.) f⋅g

d.) f/g

e.) g/f

a.) f+g

b.) f-g

c.) f⋅g

e.) g/f

1. f(x)= |x|; g(x)= |x-3|

a.) f+g

b.) f-g

c.) f⋅g

d.) f/g

e.) g/f

a.) f+g

b.) f-g

c.) f⋅g

d.) f/g

e.) g/f

2. f(x)=1/(x+1); g(x)=x/(x-2)

a.) f+g

b.) f-g

c.) f⋅g

d.) f/g

e.) g/f

a.) f+g

b.) f-g

c.) f⋅g

d.) f/g

e.) g/f

3. f(x)=x^2; g(x)=1/√x

a.) f+g

b.) f-g

c.) f⋅g

a.) f+g

b.) f-g

c.) f⋅g

d.) f/g

e.) g/f

e.) g/f

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Marked as Best Answer

1a. f+g = abs (x) + abs (x-3)

1b. f-g = abs (x) - abs (x-3)

1c. f*g = abs [x(x-3)]

1d. f/g = abs[x/(x-3)]

1e. g/f = abs [(x-3)/x]

2a. f+g = {[1/(x+1)] + [2/(x-2)] +1}

2b. f-g = {[1/(x+1)] -[2/(x-2)] -1}

2c. f*g = {x/[(x+1)(x-2)]}

2d. f/g = {(x-2)/[x(x+1)]}

2e. g/f = {[x(x+1)]/(x-2)}

3a. f+g = x^{2} + [1/(x^{½})]3b.

3b f-g = x2 - [1/(x½)]

3c. f*g = x^{3/2}

3d. f/g = x^{5/2}

3e. = 1(x^{5/2})

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## Comments

abs(x)+abs(x-3)No further simplification is possible.abs(x)-abs(x-3)No further simplification is possible.abs [x(x-3)]No further simplification is possible.abs[x/(x-3)]No further simplification is possible.abs [(x-3)/x]No further simplification is possible.{[1/(x+1)] + [2/(x-2)] +1}No further simplification is possible.{[1/(x+1)] - [2/(x-2)] -1}No further simplification is possible.{x/[(x+1)(x-2)]}No further simplification is possible.{(x-2)/[x(x+1)]}No further simplification is possible.{[x(x+1)]/(x-2)}No further simplification is possible(x^2) + (1/√x)(x^2) - (1/√x)xor^{3/2}[(x)*(√x)]xor^{5/2}[(x^2)*(√x)](1/xor^{5/2})x^{-5/2}