Correct Answer:
Even Function
Solution:
For an even function:
f(x) = f(-x)
For an odd function:
f(x) = -f(x)
The given function is:
[tex]f(x)= x^{6} + 10x^{4}- 11 x^{2}+19 [/tex]
Replacing x by -x, we get:
[tex]f(-x)= (-x)^{6} + 10(-x)^{4}- 11 (-x)^{2}+19 \\ \\
f(-x)= x^{6} + 10x^{4}- 11 x^{2}+19 \\ \\
f(-x) = f(x)
[/tex]
Since f(-x) = f(x), the given function is an even function.
