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aniked [119]
3 years ago
9

Why is f(x)=0 the only odd and even function?

Mathematics
2 answers:
kupik [55]3 years ago
6 0
F is odd if and only f f(-x) = -f(x) so f(x) = 0 works because 0 = 0 always.

f is even if and only if f(-x) = f(x) so f(x) = 0 works because there's no x term so nothing changes. 0 = 0.
inessss [21]3 years ago
3 0
If f is even, then f(-x) = f(x) for all x in the domain
If f is odd, then f(-x) = -f(x) for all x in the domain

Use substitution to find that...
f(-x) = -f(x)
f(x) = -f(x) <<--- replaced f(-x) on the left side with f(x)
f(x)+f(x) = 0 <<--- add f(x) to both sides and isolate f(x)
2*f(x) = 0
f(x) = 0

So if x is both even and odd at the same time, then f(x) = 0 for all values of x in the domain of f. This produces a flat horizontal line through the origin. It is both symmetric with respect to the y axis and it has origin symmetry as well (we can rotate it 180 degrees around the origin to have it line up with itself)

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Step-by-step explanation:

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2 years ago
When do u use two number lines to compare two fractions
jeka94

Answer:

You need two number lines to compare two fractions when their denominators are different. The procedure is that you draw to segment lines of the same length but divede each line according to its denominator and then compare the place of the points that mark the fraction numbers, the line that content the marke further away from the start end will be indicate the greater fraction. For example, the fractions 3/4 and 7/10. One line will be divided inot 4 equidistant segments, and the other with 10 equidistant segments. The fraction 3/4 will be represented with 3 marks on the first line, and the fraction 7/10 will be represented with 7 marks on the second line. Now you can compare the size of the two segments marked adn decide which fraction is greater.

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5 0
3 years ago
What is the quotient when the sum of 13 and 11 is divided by the difference of 13 and 11
Andreyy89

Answer:

12

Step-by-step explanation:

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Hope this helps!

7 0
3 years ago
Read 2 more answers
Zev has 36 pencils and 45 erasers. He wants to use all of the pencils and erasers to make identical packages for his friends. Wh
soldier1979 [14.2K]

Answer:

Step-by-step

If you don't want to have anything left over, then the highest common factor is

36: 2 * 2 * 3 * 3

45: 3 * 3 * 5

The highest common factor is 9.

So he can make nine packages with

4 pencils in each one and

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3 0
3 years ago
The resale value of a bike decreases by 14% per year. A new bike is valued at $350. Approximate the resale value after 4 years t
Ray Of Light [21]

Answer: $‭191.45

Step-by-step explanation:

This question requires the price of a bike in future so you can use the future value formula to calculate it:

Future value = Amount * (1 + rate)^ no. of periods

= 350 * (1 - 14%)⁴

= 350 * ‭0.54700816‬

= $‭191.45

<em>The rate is subtracted from 1 instead of being added to represent that the value is decreasing not increasing. </em>

7 0
3 years ago
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