Is \(f(x) = \frac{3}{2x^{6}-5} \) an even function, odd function, or neither?
+796 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.
+9479 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.
