# CAT 2014 | Question: 33

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Use the following information for next two questions:

A function $f(x)$ is said to be even if $f(-x) = f(x)$, and odd if $f(-x) = -f(x)$. Thus, for example, the function given by $f(x)=x^{2}$ is even, while the function given by $f(x)=x^{3}$ is odd. Using this definition, answer the following questions.

The sum of two odd functions

1. is always an even function
2. is always an odd function
3. is sometimes odd and sometimes even
4. may be neither odd nor even

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the answer is always an odd function........

let f(x) and g(x) be two odd functions

then h(x) = f(x)+g(x) => h(-x) = -f(x)-g(x) =-(f(x)+g(x)) =-h(x)

which clearly indicates that h(x) is an odd function
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