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I need help with part C. I know a is an even function and b is an odd function. I don’t know what type of function part C is. Please solve algebraically! :)

Guest Sep 6, 2018
edited by Guest  Sep 6, 2018
 #1
avatar+91381 
+2

C.     h(x)  =   f(x) * g(x) /   x   =   

 

[ x^4 - 2x^2 ] * [ x^5 + x ] / [2x ]  =

 

x^2 * [ x^2 -2] * x  * [ x^4 + 1 ]  / [ 2x] =

 

x^2 * [ x^2 - 2] * [ x^4 + 1 ] / 2  =

 

[ x^4 - 2x^2 ] [ x^4 + 1 ] / 2 =

 

[x^8 - 2x^6 + x^4 - 2x^2] /2.....notice that this is an even function because replacing x  with  -x   gives back the same function

 

Also.....the graph is symmetric with the y axis which is a characteristic of even  functions...here"s the graph :

 

https://www.desmos.com/calculator/setikvzes3

 

cool cool cool

CPhill  Sep 6, 2018
edited by CPhill  Sep 6, 2018
 #2
avatar+2796 
+2

In general suppose you have an odd function o(x), and an even function e(x).

 

o(x)o(x) will be even

 

o(x)e(x) will be odd

 

e(x)e(x) will be even

 

here f(x) is even, g(x) is odd, and 1/x is odd

 

so we have the product of 2 odd and 1 even functions which by above will be even

Rom  Sep 6, 2018

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