+0  
 
0
42
2
avatar+363 

If f(x) and g(x) are odd functions, show that the composite function f(g(x)) is also odd.

AdamTaurus  Oct 10, 2017
Sort: 

2+0 Answers

 #1
avatar+4749 
+2

I want to know how to do this problem too.....

hectictar  Oct 10, 2017
 #2
avatar+90610 
+3

This is not likely to be a very good 'proof' but here goes.

 

since f(x) and g(x) are odd funtion,

\(f(-x)=-f(x)\)            and      \(g(-x)=-g(x)\)

 

Let  \(x_1\)  be a point such that    

\(a=g(x_1)   \qquad     -a=g(-x_1)\)

 

\(f(g(x_1))=f(a) \qquad f(g(-x_1))=f(-g(x_1))=f(-a)=-f(a)\\ so\\ f(-g(x_1))=-f(g(x_1)) \\ \text{by definition this means that }f(g(x)) \text{ is an odd function.}\)

Melody  Oct 10, 2017

3 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details