SOLUTION: For the functions f(x) and g(x), determine the domain of (fg)(x) (the product of f and g). f(x)=2/x-12, g(x)=-6x-5. a) x is a real number. b) x is a real number and x is not e

Algebra ->  Rational-functions -> SOLUTION: For the functions f(x) and g(x), determine the domain of (fg)(x) (the product of f and g). f(x)=2/x-12, g(x)=-6x-5. a) x is a real number. b) x is a real number and x is not e      Log On


   

Question 260502: For the functions f(x) and g(x), determine the domain of (fg)(x) (the product of f and g). f(x)=2/x-12, g(x)=-6x-5.
a) x is a real number.
b) x is a real number and x is not equal to 5.
c) x is a real number and x is not equal to -12.
d) x is a real number and x is not equal to 12.
If my understanding is correct, the answer would be option a. Is this correct? Please explain.
Found 2 solutions by drk, stanbon:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=2/(x-12), g(x)=-6x-5.
%28fg%29%28x%29+=+%28-12x-10%29%2F%28x-12%29
Since there is an x in the denominator we set it = 0 and solve.
x -12 = 0
x = 12
This tells us that our domain is all reals EXCEPT 12
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based on the answers, it is [D]

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
For the functions f(x) and g(x), determine the domain of (fg)(x) (the product of f and g). f(x)=2/x-12, g(x)=-6x-5.
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(fg)x = ([2/(x-12)][-6x-5]
= (-12x-10)/(x-12)
a) x is a real number.
b) x is a real number and x is not equal to 5.
c) x is a real number and x is not equal to -12.
d) x is a real number and x is not equal to 12.
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The denominator cannot be zero.
Ans: d
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Cheers,
Stan H.