JEE Exam > JEE Videos > Sets and Functions > F(x) = 0: Even or Odd?
F(x) = 0: Even or Odd? Video Lecture | Sets and Functions - JEE
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FAQs on F(x) = 0: Even or Odd? Video Lecture - Sets and Functions - JEE
| 1. Is the function F(x) = 0 even or odd? |  |
Ans. The function F(x) = 0 is an even function. This is because an even function is defined as f(x) = f(-x) for all values of x. In this case, when we substitute -x for x in the function F(x) = 0, we still get F(-x) = 0, which means the function remains unchanged. Therefore, F(x) = 0 is an even function.
| 2. What is the significance of a function being even or odd? | |
Ans. The significance of a function being even or odd lies in its symmetry properties. An even function exhibits symmetry about the y-axis, meaning that if we reflect the graph of the function across the y-axis, it remains unchanged. On the other hand, an odd function exhibits symmetry about the origin, meaning that if we rotate the graph of the function by 180 degrees about the origin, it remains unchanged. These properties help us understand certain characteristics of functions and simplify calculations.
| 3. Can a function be both even and odd at the same time? | |
Ans. No, a function cannot be both even and odd at the same time. By definition, an even function satisfies f(x) = f(-x) for all values of x, while an odd function satisfies f(x) = -f(-x) for all values of x. These two conditions are mutually exclusive. Therefore, a function can only be either even or odd, but not both simultaneously.
| 4. What are some examples of even functions? | |
Ans. Some examples of even functions include f(x) = x^2, f(x) = |x| (absolute value function), and f(x) = cos(x). In each of these examples, when we substitute -x for x, the function remains the same, satisfying the condition of evenness.
| 5. Are all constant functions even? | |
Ans. Yes, all constant functions are even. A constant function is defined as f(x) = c, where c is a constant value. For any value of x, the function f(x) will always be equal to c, irrespective of the sign of x. Therefore, when we substitute -x for x, the function remains unchanged, satisfying the condition of evenness.
Text Transcript from Video
determine whether the function f of x
equals zero is even odd or neither pause
this video and give this problem a try
let's walk through the solution the
answer to this problem is that f of X is
both an even function and an odd
function since f of X is a constant
function
therefore F of negative x also equals 0
since f of X equals 0 negative of f of X
also equals 0 therefore f of negative x
equals f of X as well as negative of f
of X so the given function is even as
well as odd the graph of this function
lies along the x axis and is symmetric
about the origin as well as the y axis
in fact f of x equals 0 is the only real
function that is both an even function
and an odd function
equals zero is even odd or neither pause
this video and give this problem a try
let's walk through the solution the
answer to this problem is that f of X is
both an even function and an odd
function since f of X is a constant
function
therefore F of negative x also equals 0
since f of X equals 0 negative of f of X
also equals 0 therefore f of negative x
equals f of X as well as negative of f
of X so the given function is even as
well as odd the graph of this function
lies along the x axis and is symmetric
about the origin as well as the y axis
in fact f of x equals 0 is the only real
function that is both an even function
and an odd function
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Nov 23, 2024 Last updated |
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