Find the domain of the coposite function f@gf(x)=5/(x+9)g(x)=x+6

Falak Kinney 2020-11-24 Answered

Find the domain of the coposite function fg
f(x)=5x+9
g(x)=x+6

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Expert Answer

faldduE
Answered 2020-11-25 Author has 109 answers
The value of fg is:
f(g(x))=f(x+6)
=5(x+6)+9
=5x+15
therefore the composite function fog is:f(g(x))=5x+15
as we know that the domain of the function is the set of values of the independent variable for which the function is defined.
so we can notice that the composite function fg is defined when the denominator of fg is not equal to zero.
that implies
x+150
x15
therefore the composite function fg is defined for all values of x except x=-15.
therefore the domain of the composite function fg is :{xx15}
therefore the second option is correct.
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