Question

A function f(x) is said to be odd if, f(-x)= f(x)Select one:
a-True
b-false ​

Answer 1

The statement is false; a function f(x) is considered to be odd if it satisfies the condition f(-x) = -f(x), not f(-x) = f(x), which defines an even function.

Step-by-step explanation:

The statement given is false. For a function f(x) to be considered an odd function, it must satisfy the condition f(-x) = -f(x). This is because an odd function is symmetric with respect to the origin, meaning that reflecting the function about the y-axis and then about the x-axis produces the original function. An example of this is the function xe-x², which is odd because it is the product of an odd function (x) and an even function (e-x²).

In contrast, an even function satisfies the condition f(-x) = f(x), which means it is symmetric about the y-axis. Therefore, when discussing the concept of symmetrical functions, it is important not to confuse the criteria for even and odd functions.