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A function f(t) is an even function, if for all values of (t)
( T is the time-period of the function)
- a)f (t) = f ( t + T/2)
- b)f (t) = - f (t + T/2)
- c)f (t) = f (-t)
- d)f (t) = - f (-t)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A function f(t) is an even function, if for all values of (t)( T is th...
Explanation:
An even function is a function that has symmetry about the y-axis. Mathematically, a function f(t) is even if f(t) = f(-t) for all values of t.
Let's go through each option and see if it satisfies the definition of an even function.
a) f(t) = f(t + T/2)
This option states that the function is equal to itself after a time period of T/2. However, this does not guarantee symmetry about the y-axis. Therefore, option a) is not correct.
b) f(t) = -f(t + T/2)
This option states that the function is equal to its negative value after a time period of T/2. This does not satisfy the definition of an even function because f(t) is not equal to f(-t). Therefore, option b) is not correct.
c) f(t) = f(-t)
This option states that the function is equal to itself when t is replaced by -t. This satisfies the definition of an even function because f(t) = f(-t) for all values of t. Therefore, option c) is correct.
d) f(t) = -f(-t)
This option states that the function is equal to its negative value when t is replaced by -t. This does not satisfy the definition of an even function because f(t) is not equal to f(-t). Therefore, option d) is not correct.
In conclusion, the correct answer is option c) because it satisfies the definition of an even function.
An even function is a function that has symmetry about the y-axis. Mathematically, a function f(t) is even if f(t) = f(-t) for all values of t.
Let's go through each option and see if it satisfies the definition of an even function.
a) f(t) = f(t + T/2)
This option states that the function is equal to itself after a time period of T/2. However, this does not guarantee symmetry about the y-axis. Therefore, option a) is not correct.
b) f(t) = -f(t + T/2)
This option states that the function is equal to its negative value after a time period of T/2. This does not satisfy the definition of an even function because f(t) is not equal to f(-t). Therefore, option b) is not correct.
c) f(t) = f(-t)
This option states that the function is equal to itself when t is replaced by -t. This satisfies the definition of an even function because f(t) = f(-t) for all values of t. Therefore, option c) is correct.
d) f(t) = -f(-t)
This option states that the function is equal to its negative value when t is replaced by -t. This does not satisfy the definition of an even function because f(t) is not equal to f(-t). Therefore, option d) is not correct.
In conclusion, the correct answer is option c) because it satisfies the definition of an even function.
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Community Answer
A function f(t) is an even function, if for all values of (t)( T is th...
For even function, f(t) = f(-t)
For odd function, f(t) = -f(-t)
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