The function F is an odd function.
What are odd functions and even functions?
A function f(x) is even if f(-x) = f(x), for all values of x in D(f) and it is odd if f(-x) = -f(x), for all values of x. The graph even function is symmetric with respect to the y-axis and the graph of an odd function is symmetric about the origin.
According to the question
Function F(x) = [tex]8x^5+4x^3+5x[/tex]
To check whether function is odd or even
Let x = -x
Now, Substituting -x in f(x)
F(-x) = [tex]8(-x)^5+4(-x)^3+5(-x)[/tex]
i.e
F(-x) = [tex]-8x^5-4x^3-5x[/tex]
or
F(-x) = [tex]-(8x^5+4x^3+5x)[/tex]
F(-x) = - F(x)
As per definition of odd function
if f(-x) = -f(x), for all values of x. it is a odd function
Therefore, it is a odd function
When graph will be plotted
We can observe that symmetry about the origin.
Hence, the function F is an odd function.
To know more about odd function and even function here:
https://brainly.com/question/14264818
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