SOLUTION: Evaluate and give the domain. f(x)= 16-x^2 g(x)= 4-x Find f(x)/g(x)

Algebra ->  Functions -> SOLUTION: Evaluate and give the domain. f(x)= 16-x^2 g(x)= 4-x Find f(x)/g(x)      Log On


   

Question 119983: Evaluate and give the domain.
f(x)= 16-x^2 g(x)= 4-x
Find f(x)/g(x)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29%2Fg%28x%29 Start with the given composition


%2816-x%5E2%29%2F%284-x%29 Plug in f%28x%29=16-x%5E2 and g%28x%29=+4-x

%28%284%2Bx%29%284-x%29%29%2F%284-x%29 Factor 16-x%5E2 to get %284%2Bx%29%284-x%29


%284%2Bx%29%284-x%29%2F%284-x%29 Combine the fractions


%284%2Bx%29cross%28%284-x%29%29%2Fcross%28%284-x%29%29 Cancel like terms


4%2Bx Simplify


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Answer:

So %2816-x%5E2%29%2F%284-x%29 simplifies to 4%2Bx . In other words %2816-x%5E2%29%2F%284-x%29=4%2Bx



So the domain of 4%2Bx is x can be any number except x cannot be equal to 4 since that makes the denominator zero for %2816-x%5E2%29%2F%284-x%29