A function is considered odd if it satisfies the property f(-x) = -f(x) for all x in the domain of the function.
Let's check each function:
f(x) = x/x^8 + 8x^4 - 7
Since the function does not have a clear negative sign term or an even exponent on x, it is not odd.
f(x) = x^3 + 4x
We have:
f(-x) = (-x)^3 + 4(-x) = -x^3 - 4x
-f(x) = -(x^3 + 4x) = -x^3 - 4x
Since f(-x) = -f(x), this function is odd.
f(x) = 3x^5 + 6x^4 + 4
Since the function does not have a clear negative sign term or an even exponent on x, it is not odd.
f(x) = 8x^2 - 8
We have:
f(-x) = 8(-x)^2 - 8 = 8x^2 - 8
-f(x) = -(8x^2 - 8) = -8x^2 + 8
Since f(-x) = -f(x), this function is odd.
The odd functions are:
f(x) = x^3 + 4x
f(x) = 8x^2 - 8
Which of the following functions are odd? Select all that apply
f(x)=x/x^8+8x^4-7
f(x)=x^3+4x
f(x)=3x^5+6x^4+4
f(x)=8x^2-8
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