CBSE Class 11-science Answered
Question is as below :
Asked by spuneet23 | 20 Sep, 2010, 05:16: PM
Expert Answer
Dear Student,
Firstly let y = 0,
then we have
f(x+0) + f(x-0) = 2f(x).f(0)
=> 2f(x) = 2f(x).f(0)
=> f(0) = 1 --------------- (1)
Now, putting x = 0, we get
f(0+y) + f(0-y) = 2f(0).f(y)
=> f(y) + f(-y) = 2f(y) (as f(0) = 1 from (1))
=> f(-y) = 2f(y) - f(y)
=> f(-y) = f(y)
or equivalently, f(x) = f(-x)
Hence f(x) is an even function.
Therefore, option b is correct.
Regards Topperlearning.
Answered by | 20 Sep, 2010, 09:22: PM
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