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Fittoniya [83]
3 years ago
10

Given f(x)=1/x+3 and g(x)=6/x+4, find the domain of f(g(x))

Mathematics
1 answer:
Murljashka [212]3 years ago
4 0

Answer:

The domain is all real numbers except the value of x=-6

Step-by-step explanation:

we have

f(x)=\frac{1}{x+3}

g(x)=\frac{6}{x+4}

we know that

f(g(x))=\frac{1}{(\frac{6}{x+4})+3}

f(g(x))=\frac{1}{\frac{6+3(x+4)}{x+4}}

f(g(x))=\frac{x+4}{6+3x+12}

f(g(x))=\frac{x+4}{3x+18}

f(g(x))=\frac{x+4}{3(x+6)}

Remember that the denominator cannot be equal to zero

so

The value of x cannot be equal to -6

therefore

The domain is all real numbers except the value of x=-6

In interval notation the domain is

(-∞,-6) ∪ (-6,∞)

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