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Is \(f(x) = \frac{3}{2x^{6}-5} \) an even function, odd function, or neither?

 Jul 28, 2019
 #1
avatar+773 
+4

https://www.desmos.com/calculator/ngvnbtqkj5 use this link to help because i don't know exactly what the graph means you are in algebra 2 and thats what i will start next week.

 Jul 28, 2019
 #2
avatar+773 
+3

mabey some one can help.

travisio  Jul 28, 2019
 #4
avatar+103715 
+2

Travisio,

Your graph shows that the funtion is symmetrical about the y axis

this means that f(x)=f(-x)

and that means that the function is even

Melody  Jul 29, 2019
 #5
avatar+773 
+4

oh okay thank you Melody much appreciated

travisio  Jul 29, 2019
 #3
avatar+8725 
+5

If     f( -x )  =  f(x)     then the function is even.

If     f( -x )  =  -f(x)    then the function is odd.

 

\(f(x)\ =\ \frac{3}{2x^6-5}\)

                                           Plug in  -x  for  x

\(f(-x)\ =\ \frac{3}{2(-x)^6-5}\)

                                           And     (ab)c  =  ac bc     so     (-x)6  =  (-1)6 x6

\(f(-x)\ =\ \frac{3}{2(-1)^6x^6\,-\,5}\)

                                           Because     -1 * -1  =  1,     -1  to an even power  =  1     and so     (-1)6  =  1

\(f(-x)\ =\ \frac{3}{2x^6\,-\,5}\)

                                           Now notice that  \(f(x)\ =\ \frac{3}{2x^6-5}\)  so we can substitute  f(x)  in for  \(\frac{3}{2x^6-5}\)

\(f(-x)\ =\ f(x)\)

 

Since  f(-x)  =  f(x) ,  the function is even.

 Jul 28, 2019

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