SOLUTION: Hello! Find f + g, f - g, fg, f/g and their domains. f(x)=2/(x+3), g(x)=x/(x+3) thanks!

Algebra ->  Functions -> SOLUTION: Hello! Find f + g, f - g, fg, f/g and their domains. f(x)=2/(x+3), g(x)=x/(x+3) thanks!      Log On


   

Question 198289: Hello!
Find f + g, f - g, fg, f/g and their domains.
f(x)=2/(x+3), g(x)=x/(x+3)
thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1
f%2Bg=f%28x%29%2Bg%28x%29=2%2F%28x%2B3%29%2Bx%2F%28x%2B3%29=%282%2Bx%29%2F%28x%2B3%29


So f%2Bg=%282%2Bx%29%2F%28x%2B3%29 where the domain is: x can be any real number except x%3C%3E-3


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# 2
f-g=f%28x%29-g%28x%29=2%2F%28x%2B3%29-x%2F%28x%2B3%29=%282-x%29%2F%28x%2B3%29


So f-g=%282-x%29%2F%28x%2B3%29 where the domain is: x can be any real number except x%3C%3E-3



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# 3
fg=f%28x%29g%28x%29+=+%282%2F%28x%2B3%29%29%28x%2F%28x%2B3%29%29=%282x%29%2F%28x%2B3%29


So fg=%282x%29%2F%28x%2B3%29 where the domain is: x can be any real number except x%3C%3E-3


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# 4



So f%2Fg=2%2Fx where the domain is: x can be any real number except x%3C%3E-3 or x%3C%3E0


Note: all of the domain restrictions are to avoid division by zero.