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Sagot :
The odd functions are f(x)=x⁵-3x³+2x and f(x)=1÷x.
Given functions are f(x)=x³-x², f(x)=x⁵-3x³+2x, f(x)=4x+9 and f(x)=1÷x.
A function is said to be odd function if and only if: f(-x) = -f(x)
For every value of x in its domain.
1. f(x)=x³-x²
Substituting -x in this, we get
f(-x)=(-x)³-(-x)²
f(-x)=-x³-x²
From above we see that
f(-x)≠-f(x)
So, this function is not odd.
2. f(x)=x⁵-3x³+2x
Substituting -x in this, we get
f(-x)=(-x)⁵-3(-x)³+2(-x)
f(-x)=-x⁵+3x³-2x
f(-x)=-(x⁵-3x³+2x)
From above we see that
f(-x)=-f(x)
So, this function is odd
3. f(x)=4x+9
Substituting -x in this, we get
f(-x)=4(-x)+9
f(-x)=-4x+9
From above we see that
f(-x)≠-f(x)
So, this function is not odd.
4. f(x)=1÷x
Substituting -x in this, we get
f(-x)=1÷(-x)
f(-x)=-(1÷x)
From above we see that
f(-x)=-f(x)
So, this function is odd.
Hence, the function f(x)=f(x)=x³-x² is not odd, f(x)=x⁵-3x³+2x is odd, f(x)=4x+9 is not odd and f(x)=1÷x is odd.
Learn more about even and odd functions from here brainly.com/question/11024366
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