Which of the following is an odd function? (1) x+x^3 (2) x^3-x^2-5 (3) x^2+x^4 (4) (3 x^2)/(x^2+

Name: Problem 22, Chapter 6: The IIT Foundation series of Mathematics Class
Uploaded: 2021-06-25T15:37:23-08:00
Duration: 2 min 7 s
Channel: Bhanuteja Chintha
Description: Which of the following is an odd function? (1) x+x^3 (2) x^3-x^2-5 (3) x^2+x^4 (4) (3 x^2)/(x^2+1)

step 1 we must find the odd function from the given options our first option is f of x is equal to x pl

Question

Which of the following is an odd function? (1) $\mathrm{x}+\mathrm{x}^{3}$ (2) $x^{3}-x^{2}-5$ (3) $\mathrm{x}^{2}+\mathrm{x}^{4}$ (4) $\frac{3 x^{2}}{x^{2}+1}$

   Which of the following is an odd function?
(1) $\mathrm{x}+\mathrm{x}^{3}$
(2) $x^{3}-x^{2}-5$
(3) $\mathrm{x}^{2}+\mathrm{x}^{4}$
(4) $\frac{3 x^{2}}{x^{2}+1}$

The IIT Foundation series of Mathematics Class

Trishna Knowledge… 5th Edition

Chapter 6, Problem 22

Instant Answer

Solved by Expert Bhanuteja Chintha

06/25/2021

Step 1

An odd function is defined as a function that satisfies the condition $f(-x) = -f(x)$ for all $x$ in the domain of $f$. Show more…

Show all steps

Thanks for your feedback!

Which of the following is an odd function? (1) $\mathrm{x}+\mathrm{x}^{3}$ (2) $x^{3}-x^{2}-5$ (3) $\mathrm{x}^{2}+\mathrm{x}^{4}$ (4) $\frac{3 x^{2}}{x^{2}+1}$

Play audio

Feedback

Bhanuteja Chintha and 65 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Odd Function

An odd function is one where f(-x) = -f(x) for every x in the domain. This means that if you reflect the graph of the function across the origin, you obtain the same graph. It characterizes functions that are symmetric with respect to the origin.

Function Symmetry

Function symmetry involves evaluating how a function behaves under transformations such as reflection. In the context of odd functions, this symmetry specifically refers to being invariant under a rotation of 180 degrees about the origin, which distinguishes them from even functions that are symmetric about the y-axis.

Polynomial Functions

Polynomial functions are expressions consisting of sums of powers of x multiplied by coefficients. When analyzing the symmetry of a polynomial, particularly odd functions, one focuses on the parity of the exponents. Terms with odd exponents contribute to the oddness of the function, while even exponents contribute to evenness.

Please give Ace some feedback