CAT 1993 — QA Question 25
Even / Odd FunctionsEasy
Passage / Data
Answer the next 2 questions based on the information given below:
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) = x2 is even, while the function given by f(x) = x3 is odd. Using this definition, answer the following questions.
The sum of two odd functions
Answer & solution
- A
is always an even functions
is always an odd function
- C
is sometimes odd and sometimes even
- D
may be neither odd nor even
Solution
Let f(x) = g(x) + h(x), where g and h are odd functions.
∴ f(–x) = g(–x) + h(–x) = –g(x) – h(x) = –f(x).
Hence, f(x) is a odd function.
Hence, option (b).