Question

Which of the following functions is odd?

A) f(x)=x²
B) f(x)=sin(x)
C) f(x)=eˣ
D) f(x)=cos(x)

Answer 1

Among the options given, B) f(x) = sin(x) is the odd function, because it satisfies the condition f(-x) = -f(x) for all x in the domain.

Step-by-step explanation:

In mathematics, a function is called odd if it satisfies the condition f(-x) = -f(x) for all x in the domain of the function. This means that the function is symmetrical with respect to the origin, and that its graph is invariant under a half-turn about the origin. Conversely, a function is called even if it satisfies the condition f(-x) = f(x), which means the function is symmetrical with respect to the y-axis.

Let's analyze the given options:

• f(x) = x² is an even function, because f(-x) = (-x)² = x² = f(x).
• f(x) = sin(x) is an odd function since f(-x) = sin(-x) = -sin(x) = -f(x). This satisfies the definition of an odd function.
• f(x) = eˣ is neither odd nor even since f(-x) = e⁻ˣ does not equal ±f(x).
• f(x) = cos(x) is an even function because f(-x) = cos(-x) = cos(x) = f(x).

Therefore, the function that is odd among the options provided is B) f(x) = sin(x). It is the correct option to choose as the answer to the question about which of the functions listed is odd.