Find f x fx for the following function fx x3 x 1 fx fx

Find f( - x) - f(x) for the following function. f(x) = x^3 + x - 1 f(-x) - f(x) = (Simplify your answer. Do not factor)

Solution

Given f(X)=X³+X-1

f(-X)=(-X)³+(-X)-1

=-X³-X-1

We need to find out  f(-X) -  f(X) :

f(-X) -  f(X)=-X³-X-1-(X³+X-1)

=-X³-X-1-X³-X+1

=-2X³-2X

=-2X(X²+1)