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please refer to image

 Apr 29, 2019
 #1
avatar+7711 
+1

If the odd function is continuous, it must pass through (0,0) as the property of odd function is that the graph of the function is rotational symmetrical about the origin.

Substitute (2,-2) into g(x) = f(x+3) - 5.

\(-2 = f(5) - 5\\ f(5) = 3\)

From this, we get \(f(-5) = -3\).

When x = -8,

\(g(-8) = f(-5) - 5\\ g(-8) = -3-5 = -8\).

So it must also pass through (-8,-8).

 

Answer: (0,0), (-8,-8)

 Apr 29, 2019
 #3
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+1

Max continuity is not needed

 

EDIT: I don't think g(x) must pass through (0,0), f must pass through that point

 

g(x) will pass through (-3,-5)

Guest Apr 30, 2019
edited by Guest  Apr 30, 2019
 #2
avatar+44 
-1

This kid of looks like its a problem for AOPS. (I'm just going to assume it is) You can always ask on message boards, or read the textbook if it is.

 Apr 29, 2019

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