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Even and Odd Function - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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Even and Odd Function is considered one the most difficult concept.
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22 Questions around this concept.
Solve by difficulty
A function $f$ from the set of natural numbers to integers defined by $f(n)=\left\{\begin{array}{l}\frac{n-1}{2}, \text { when } n \text { is odd } \\ -\frac{n}{2}, \text { when } n \text { is even }\end{array}\right.$ is
The function is
Which of the following is the graph of an odd function?
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$f(x)=\cos x, x \in \mathbb{R}$, is a/an
$f(x)=3 x-x^3, x \in \mathbb{R}$, is a/an
The function $f(x)= cos\left ( log\left (x+\sqrt{x^{2}+1} \right ) \right ) is$
Concepts Covered - 1
Even and Odd Function
Even function:
If for a function $f(x), f(-x)=f(x)$ then the function is known as even function. Even functions are symmetric about the $y$ axis.
y = x2 y = |x| y = cos(x)
Odd function:
If for a function $f(x), f(-x)=-f(x)$ then the function is known as odd function. Odd functions are symmetric about the origin.
y = sin(x) y = x3
NOTE: We can have functions that are neither even nor odd. Eg, $\mathrm{y}=\mathrm{x}+1$
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