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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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Two circles of radius 1 are centered at $(4,0)$ and $(-4,0).$ How many circles are tangent to both of the given circles and also
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Answer:

1 circle

Step-by-step explanation:

Given two circles (red circles on the diagram).

There are two tangent circles to both of the given circles (blue circles on the diagram), and only one of them is passing through the point (0,5).

Let's check it.

The equations of the tangent circles are

x^2+y^2=9\ [\text{Smaller tangent circle}]\\ \\x^2+y^2=25\ [\text{Larger tangent circle}]

Check whether point (0,5) lies on the smaller circle:

0^2 +5^2 =0+25=25\neq 9

No

Check whether point (0,5) lies on the larger circle:

0^2 +5^2 =0+25=25

Yes

<u>Answer: </u>1 circle

7 0
3 years ago
Simplify (3 + 2i)(7 − 5i).
erma4kov [3.2K]
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