what is an equation of the line perpendicular to y+1=-3(x-5) and passes through (4,-6)? please help quick
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The domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.
<h3>What is a function?</h3>It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
f(x) = 1/√x
m(x) = x² - 4
Domain of f(x)/m(x):
f(x)/m(x) = (1/√x)/(x² - 4)
f(x)/m(x) = 1/√x(x² - 4)
The denominator cannot be zero:
√x(x² - 4) ≠ 0
x(x - 2)(x+2) ≠ 0
x ≠ 0, 2, -2
and x > 0
Domain of f(x)/m(x) is: (0, ∞) - {0, 2, -2} or
Domain of f(m(x)):
f(m(x)) = 1/√(x² - 4)
x² - 4 > 0
Domain:
Domain of m(f(x)):
= ((1/√x)² - 4)
Domain:
Thus, the domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.
Learn more about the function here:
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Answer:
31
Step-by-step explanation:
The series are given as geometric series because these terms have common ratio and not common difference.
Our common ratio is 2 because:
1*2 = 2
2*2 = 4
The summation formula for geometric series (r ≠ 1) is:
or
You may use either one of these formulas but I’ll use the first formula.
We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.
Therefore, the solution is 31.
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Summary
If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.
Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:
Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:
Above should be applied for series that have common ratio not equal to 1.
Above should be applied for series that have common ratio exactly equal to 1.
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Topics
Sequence & Series — Geometric Series
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Others
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