which of the following functions are odd select all that apply

Question

A f(x)=7x^5-4x
B f(x)=3x^2-9x
C f(x)=6x^7+4x^3-2
D f(x)=-5x^9+8x^5+4x^3
E f(x)2x^3+5

Answer 1

A function is odd if f(-x) = -f(x) for all x in the domain.

Let's check each function one by one:

A) f(x) = 7x^5 - 4x
f(-x) = 7(-x)^5 - 4(-x) = -7x^5 + 4x
-f(x) = -7x^5 + 4x
Since f(-x) = -f(x), this function is odd.

B) f(x) = 3x^2 - 9x
f(-x) = 3(-x)^2 - 9(-x) = 3x^2 + 9x
-f(x) = -3x^2 + 9x
Since f(-x) is not equal to -f(x), this function is not odd.

C) f(x) = 6x^7 + 4x^3 - 2
f(-x) = 6(-x)^7 + 4(-x)^3 - 2 = -6x^7 - 4x^3 - 2
-f(x) = -6x^7 - 4x^3 + 2
Since f(-x) = -f(x), this function is odd.

D) f(x) = -5x^9 + 8x^5 + 4x^3
f(-x) = -5(-x)^9 + 8(-x)^5 + 4(-x)^3 = -5x^9 + 8x^5 - 4x^3
-f(x) = 5x^9 - 8x^5 - 4x^3
Since f(-x) is not equal to -f(x), this function is not odd.

E) f(x) = 2x^3 + 5
f(-x) = 2(-x)^3 + 5 = -2x^3 + 5
-f(x) = -2x^3 - 5
Since f(-x) is not equal to -f(x), this function is not odd.

So, the odd functions are A) f(x) = 7x^5 - 4x and C) f(x) = 6x^7 + 4x^3 - 2.