A function is odd if and only if f(-x) = -f(x) for every x in the domain of f.
a. f(x)=7x^5-4x
To check if it is odd, we substitute -x for x:
f(-x) = 7(-x)^5-4(-x) = -7x^5+4x
This is not equal to -f(x) = -7x^5+4x.
So, this function is not odd.
b. f(x)=3x^2-9x
To check if it is odd, we substitute -x for x:
f(-x) = 3(-x)^2-9(-x) = 3x^2+9x
This is not equal to -f(x) = -(3x^2-9x) = -3x^2+9x.
So, this function is not odd.
c. f(x)=6x^7+4x^3-2
To check if it is odd, we substitute -x for x:
f(-x) = 6(-x)^7+4(-x)^3-2 = -6x^7-4x^3-2
This is equal to -f(x) = -6x^7-4x^3-2.
So, this function is odd.
d. f(x)=-5x^9+8x^5+4x^3
To check if it is odd, we substitute -x for x:
f(-x) = -5(-x)^9+8(-x)^5+4(-x)^3 = -5x^9-8x^5-4x^3
This is equal to -f(x) = -(-5x^9+8x^5+4x^3).
So, this function is odd.
e. f(x)=2x^3+5
To check if it is odd, we substitute -x for x:
f(-x) = 2(-x)^3+5 = -2x^3+5
This is not equal to -f(x) = -(2x^3+5) = -2x^3-5.
So, this function is not odd.
Therefore, the odd functions are c. f(x)=6x^7+4x^3-2 and d. f(x)=-5x^9+8x^5+4x^3.
Which of the following functions are odd? Select all that apply.
a. f(×)=7×^5-4×
b. f(×)=3×^2-9×
c. f(×)=6×^7+4×^3-2
d. f(×)=-5×^9+8×^5+4×^3
e. f(×)=2×^3+5
1 answer