For this last problem you will be given a definition that we

For this last problem, you will be given a definition that we did not go over in class and you will be asked questions based on the definition. DEFINITIONS: A function is called odd iff -f (x) = f(-x) for all x A function is called even iff f(x) = f(-x) for all x. Which of the following functions are even? Which are odd? Which are neither? Explain your answer. f(x) = cos x f(x) = 3x^2 + 2x^24 - 6 f(x) = 3 + 2x^17 f(x) = x - 8x^5

Solution

(1)

f(-x)=cos(-x)=cos(x)=f(x)

Hence function is even

(2)

f(-x)=3(-x)^2+2(-x)^24-6=3x^2+2x^24-6=f(-x)

Hnece, function is even

(3)

f(-x)=3+2(-x)^17=3-2x^176-3-2x^17=6-f(x)

Hence function is neither even nor odd

(4)

f(-x)=-x-8(-x)^5=-x+8x^5=-f(x)

Hence function is odd