If f(x) is a real valued odd function , then which one of the following is incorrect ?A. `(f(x)-f-(-x))/(2)` is an odd function.B. `(f(x)+f(-x))/(2)` is an even function.C. `[|f(x)|+2]` is an even function, `[*]` denotes the greatest integer function.D. `(f(x)-f(-x))/(2)` is neither even nor odd.

If f(x) is a real valued odd function , then which one of the followin

1.	If f(x) is a real valued odd function , then which one of the following is incorrect ?A. `(f(x)-f-(-x))/(2)` is an odd function.B. `(f(x)+f(-x))/(2)` is an even function.C. `[\|f(x)\|+2]` is an even function, `[*]` denotes the greatest integer function.D. `(f(x)-f(-x))/(2)` is neither even nor odd.
Answer» Correct Answer - D We observe that `phi(x)=(f(x)+f(-x))/(2)` is an even function . `and Psi(x)=(f(x)-f(-x))/(2)` is an odd functions. Let `g(x)=[\|f(x)\|+2]`. Then, `g(-x)=[\|f(-x)\|+2]` `implies g(-x)=[\|-f(x)\|+2]` `=g(-x)=[\|f(x)\|+2]` `implies g(-x)=g(x)` for all ` x in R `. Therefore, g(x) is an even function.

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