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Algebra 2 Functions operations question.

Algebra 2 Functions operations question.-example-1
User Karesh A
by
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1 Answer

5 votes

Answer:

B.
\left((f)/(g)\right)(x)=(1)/(x-2) domain is
x\in \left(-\infty, -(5)/(3)\right)\cup \left(-(5)/(3),2\right)\cup (2,\infty).

Explanation:

If
f(x)=3x+5 and
g(x)=3x^2-x-10, then


\left((f)/(g)\right)(x)=(3x+5)/(3x^2-x-10)=(3x+5)/(3x^2+5x-6x-10)=(3x+5)/(x(3x+5)-2(3x+5))=(3x+5)/((3x+5)(x-2)).

Note that the denominator cannot be equal to 0, so


3x+5\\eq 0 \text{ and } x-2\\eq0\\ \\x\\eq-(5)/(3)\text{ and }x\\eq 2.

If
x\in \left(-\infty, -(5)/(3)\right)\cup \left(-(5)/(3),2\right)\cup (2,\infty), then


\left((f)/(g)\right)(x)=(3x+5)/((3x+5)(x-2))=(1)/(x-2).

User Astrochris
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