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Question

Which of the following is an even funciton
Here [.] denotes the greatest inetger function and fis any function.
  1. [x]x
  2. f(x)f(x)
  3. f(x)+f(x)
  4. e32xtan2x

A
[x]x
B
e32xtan2x
C
f(x)+f(x)
D
f(x)f(x)
Solution
Verified by Toppr

Let f(x) be any function.

Therefore

If f(x) is an odd function

h(x)=f(x)+f(x)

=0 ...(i)

If f(x) is an even function

h(x)=f(x)+f(x)

h(x)=2f(x) ...(ii)

From i and ii we see that h(x) is always an even function.

Hence f(x)+f(x) will be even function.

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