Homework 4 P 18SolutionIf fx fx fx is odd O fx fx fx is

Homework 4 P 18

Solution

If f(-x) = -f(x) ; f(x) is odd ---> O

f(-x) = f(x) ; f(x) is even ----> E

1 . f(x) = x^4 +3x^6 +2x^9

f(-x) = (-x)^4 +3(-x)^6 +2(-x)^9 = x^4 +3x^5 -2x^9

neithe even nor odd

N

2. f(x) = -5x^4 -3x^6 -2

f(-x) = -5(-x)^4 -3(-x)^6 -2 = -5x^4 -3x^6 -2

= f(x)

So, even function

E

3) f(x) = x^3 +x^3 +x^9

f(-x) = (-x)^3 +(-x)^3 +(-x)^9

= -x^3 -x^3 -x^9 = -( x^3 +x^3 +x^9)

= -f(x)

So, odd function

O

4) f(x) = x^4 -6x^6 +3x^2

f(-x) = (-x)^4 -6(-x)^6 +3(-x)^2

= x^4 -6x^6 +3x^2

= f(x)

Even function

E