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Question 596780: Find the domain of the function and express the answer in interval notation. Explain in words or show the calculations.
a.f(x)=sqrt4x+12
b.g(x)= x^2/x+12
c.f(x)= 10x^2+19x-5
d.g(x)=15/x
e.f(x)=sqrt x-15
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the domain of the function and express the answer in interval notation. Explain in words or show the calculations.
a.f(x)=sqrt4x+12
b.g(x)= x^2/x+12
c.f(x)= 10x^2+19x-5
d.g(x)=15/x
e.f(x)=sqrt x-15
**
Two rules apply here: radicand≥0 and f(x) is undefined when denominator=0
..
a.f(x)=sqrt(4x+12)
4x+12≥0
4x≥-12
x≥-1/3
domain: [-1/3,∞)
..
b.g(x)= x^2/x+12
x+12=0
x≠-12
domain: (-∞,-12) U (-12,∞)
..
c.f(x)= 10x^2+19x-5
domain: (-∞,∞)
..
d.g(x)=15/x
x≠0
domain: (-∞,0) U (0,∞)
..
e.f(x)=sqrt (x-15)
x-15≥0
x≥15
domain: [15,∞)
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