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**+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

CPhill
Sep 6, 2018