Question 987361: Let f(x)= x^2 - 16 and g(x)= x - 4. What are f*g and f/g ? What are their domains?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! f*g means multiply the functions.
(x^2-16)(x-4)=x^3-4x^2-16x+64.
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f/g means divide the functions
(x^2-16)/(x-4), but the numerator is a difference of squares, (x+4)(x-4), and the last cancels the denominator.
f/g=(x+4)
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Domains of a composite function are the domains that satisfy both.
f(x) has domain of all reals.
g(x) does too.
Their composite domain is all reals
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In the second, the denominator is (x-4). The function doesn't exist at x=4, regardless of what can be factored. Therefore, the domain of f/g is all reals except x=4.
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