Consider the following functions. f(x) = 36 − x2 , g(x) = 1 + x Find (f +

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Consider the following functions.

f(x) = 
36 − x2
,   g(x) = 
1 + x
Find 
(f + g)(x)

 

Find the domain of 
(f + g)(x).
 (Enter your answer using interval notation.)
 

Find 
(f − g)(x).

 

Find the domain of 
(f − g)(x).
 (Enter your answer using interval notation.)
 

Find 
(fg)(x).

 

Find the domain of 
(fg)(x).
 (Enter your answer using interval notation.)
 

Find 
f
g
(x).

 

Find the domain of 
f
g
(x).
 (Enter your answer using interval notation.)
 
Jun 30th, 2015

Thank you for the opportunity to help you with your question!

we have f(x) = 36 - x² and g(x) = 1 + x

so : 

1) - (f + g)(x) = (36 - x²) + (1 + x) = -x² + x + 37 

and the domain is :  D(f+g) =  IR = ]-infini , 0]U[0, +infini[  

2) -  (f - g)(x) = (36 - x²) - (1 + x) = - x² - x + 35  

and the domain is : D(f - g) = IR =  ]-infini , 0]U[0, +infini[  

3) - (fg)(x) = (36 - x²) * (1 + x)  = 36 + 36x - x² - x^3 = - x^3  - x²  + 36x + 36 

and the domain is :  D(fg) = IR =  ]-infini , 0 ] U [ 0, +infini[  

4) - (f/g)(x) = (36 - x²) / (1 + x) =  (- x² + 36) / ( x + 1)

and the domain is : D(f/g) = {x c IR /  x + 1 =/= 0 } 

so : D(f/g) = {x c IR /  x =/= -1 } 

so :  D(f/g) = ]- infini , -1 ] U [-1 , + infini [

if you dont understand something just ask , 

and 

Please Each time you have any others homework invite me first i will give you the best answers 

Good Luck 


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 30th, 2015

we have f(x) = 36 - x² and g(x) = 1 + x

so : 

1) - (f + g)(x) = (36 - x²) + (1 + x) = -x² + x + 37 

and the domain is :  D(f+g) =  IR = ]-infinity , 0]U[0, +infinity[  

_____________________________________________

2) -  (f - g)(x) = (36 - x²) - (1 + x) = - x² - x + 35  

and the domain is : D(f - g) = IR =  ]-infinity , 0]U[0, +infinity[  

_____________________________________________

3) - (fg)(x) = (36 - x²) * (1 + x)  = 36 + 36x - x² - x^3 = - x^3  - x²  + 36x + 36 

and the domain is :  D(fg) = IR =  ]-infinity , 0 ] U [ 0, +infinity[  

_____________________________________________

4) - (f/g)(x) = (36 - x²) / (1 + x) =  (- x² + 36) / ( x + 1)

and the domain is : D(f/g) = {x c IR /  x + 1 =/= 0 } 

so : D(f/g) = {x c IR /  x =/= -1 } 

so :  D(f/g) = ]- infinity , -1 ] U [-1 , + infinity [

_______________________________________________

if you dont understand something just ask , 

and 

Please Each time you have any others homework invite me first i will give you the best answers 

Good Luck 


Jun 30th, 2015

sqrt 36

Jun 30th, 2015

What you mean with sqrt (36)  ???

Jun 30th, 2015

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