Answer:
-f(-x) = f(x)
Step-by-step explanation:
Given function is:
f(x)= -2x^5+x^3-7x
To check if a function is even, it is checked that:
f(-x)=f(x)
If f(-x) gives the original function then the function is said to be even.
And if:
-f(-x)=f(x)
which means if –f(-x) gives the original function, then the function is odd. So a function has to satisfy this rule to be an odd function.
Now for the given function:
-f(-x)= -[-2(-x)^5+(-x)^3-7(-x)]
= -[(-2)(-x^5 )+(-x^3 )+7x]
= -( 2x^5- x^3+7x)
Multiplying the negative sign
-f(-x)= -2x^5+x^3-7x
-f(-x)=f(x)
So, the function satisfies this rule to be an odd function. ..
