Answer:
(-∞, -4] ∪ [5, ∞)
Step-by-step explanation:
Hi!
Alright, so greater (or less) than or equal to is denoted with a bracket.
If x is less than or equal to -4, then the bracket is on the left side.
(___, -4]
Because x is <em>any</em> number under or equal to -4, x can range from negative infinity. However, we use a parentheses for infinity because infinity can never truly be reached.
So, x 
-4 = (-∞, -4]
X
5
Equal to = bracket
X is any number above 5, so
[5, ∞)
Because we want both of these, we use the union sign (∪)
so,
= (-∞, -4] ∪ [5, ∞)
A function
is periodic if there is some constant
such that
for all
in the domain of
. Then
is the "period" of
.
Example:
If
, then we have
, and so
is periodic with period
.
It gets a bit more complicated for a function like yours. We're looking for
such that
Expanding on the left, you have
and
It follows that the following must be satisfied:
The first two equations are satisfied whenever
, or more generally, when
and
(i.e. any multiple of 4).
The second two are satisfied whenever
, and more generally when
with
(any multiple of 10/7).
It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when
is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.
Let's verify:
More generally, it can be shown that
is periodic with period
.
Step-by-step explanation:
doyy7p57ediyfir7esusyig868surzydgkhipoti8tuiyi6ryi5iyruruoyripitsyrahfzofuuts
10 × 30 = 300
(20 characters thing)
I’m Not good at This but I’ll try to help ;c
