SOLUTION: hi, I have to determine if this function is even odd or neither...I believe is even because of the {{{x^4}}} in {{{f(x)=6x^4+5x-3}}} but i am not sure can someone please help? than

Algebra ->  Functions -> SOLUTION: hi, I have to determine if this function is even odd or neither...I believe is even because of the {{{x^4}}} in {{{f(x)=6x^4+5x-3}}} but i am not sure can someone please help? than      Log On


   

Question 85167: hi, I have to determine if this function is even odd or neither...I believe is even because of the x%5E4 in f%28x%29=6x%5E4%2B5x-3 but i am not sure can someone please help? thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A function is even when this is true

f%28x%29=f%28-x%29 where in this case f%28x%29=6x%5E4%2B5x-3 and f%28-x%29=6%28-x%29%5E4%2B5%28-x%29-3

so lets pick any number to plug in for x, say x=2

6%282%29%5E4%2B5%282%29-3=6%28-2%29%5E4%2B5%28-2%29-3 Plug in x=2

6%2816%29%2B5%282%29-3=6%2816%29%2B5%28-2%29-3 Raise 2 and -2 to the 4th power

96%2B10-3=96-10-3 Multiply

103=83 Combine like terms

Since this equation is false, the function is not even

It turns out that if you have a sum of an even function (in this case 6x%5E4) and an odd function (in this case 5x) then the function is neither even nor odd. So that means the function f%28x%29=6x%5E4%2B5x-3 is neither even nor odd. So it doesn't matter if there is an x%5E4 in the function. If there was only an x%5E4 in the function, and nothing else, then the function would be even.