Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
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
#SPJ4
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
