What is the meaning of the last equation in words?

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Homework Statement


the function decribed by
f(x) = (2, -2<x<2
= (0, 2<x<6

and f(x) = f(x+8)

Q1, what does the last equation mean in words?
Q2, how do i sketch the graph of the function f(x) over 3 periods?
Q4, is it odd or even?

Homework Equations





The Attempt at a Solution

 
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The rules of the forum are that you need to attempt to answer these before anyone can help. It just has to be an attempt. What would a function that satisfies f(x)=f(x+8) look like? Any opinions?
 
Ma77yD182 said:

Homework Statement


the function decribed by
f(x) = (2, -2<x<2
= (0, 2<x<6

and f(x) = f(x+8)

Q1, what does the last equation mean in words?
Q2, how do i sketch the graph of the function f(x) over 3 periods?
Q4, is it odd or even?

Homework Equations





The Attempt at a Solution

Can you use those to find f(7)? Hint: 7= -1+ 8.
 
It's period will become 8 (obvious).
And determine odd or even function:
if f(-x) = f(x) then even function
if f(-x) = -f(x) then odd function.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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