Define the following functions.

Question

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

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

 

3. f(x)=x^2; g(x)=1/√x

a.) f+g
b.) f-g
c.) f⋅g

d.) f/g
e.) g/f

Answer 1

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 = x² + [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)