Question

A function f(x) is said to be an odd function if
A. f(-x) = f(x)
B. f(-x) = -f(x)
C. f(-x) = k* f(x) where k is a constant
D. None of these
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Answer 1

Answer:

F(-x) = - F(x) b option

Step-by-step explanation:

Because if minus sign appeara outside it represents odd function.

Answer 2

Answer:

A function f(x) is said to be an odd function if f(-x) = -f(x).

Here option B is the correct answer.

Step-by-step explanation:

Given function is f(x). Now question is f(x) is odd for what condition.

By help of some function we can easily understand this.

Let $f(x) = x + {x}^{3} + {x}^{5} ....(1)$

So,$f( - x) = ( - x) + {( - x)}^{3} + {( - x)}^{5}$

$f( - x) = - x - {x}^{3} - {x}^{5}$

$f( - x) = - f(x)$

This is the condition of odd function.

Again we take one example,

$g(y) = {y}^{5} - {y}^{7} + {y}^{3} + y$

So,$g( - y) = {( - y)}^{5} - {( - y)}^{7} + {( - y)}^{3} + ( - y) = - {y}^{5} + {y}^{7} - {y}^{3} - y = - ( {y}^{5} - {y}^{7} + {y}^{3} + y) = - g(y)$

g(y) is odd for the condition g(-y)=-g(y).