Question

The function f(x) = -2x5 + x3 − 7x is an odd function. Which rule is satisfied by this function?

Answer 1

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. ..