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

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Consider the following functions.
f(x) = 
SQRT 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!

(f+g)(x) = SQRT (36) - x^2 + 1 - x

Domain:  All real numbers, unless the x^2 is part of the SQRT (did not specify) in which case x >= -6

(f-g)(x) = SQRT (36) - x^2 - 1 + x

Domain:  All real numbers, unless x^2 is part of SQRT in which case x>= -6

(fg)(x) = (SQRT (36) - x^2)(1 + x) = SQRT (36) + x SQRT (36) - x^2 - x^3

Domain: All real numbers, unless x^2 is part of SQRT in which case x>=-6

(f/g)(x) = (SQRT (36) - x^2)/(1+x)

Domain:  x can not equal -1, if x^2 is part of SQRT then x>= -6. otherwise, x not = 1 is the only restriction of domain.

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

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