decide whether the following statement is true or false. the cube function is odd and is increasing on the…

decide whether the following statement is true or false. the cube function is odd and is increasing on the interval (-∞,∞). choose the correct answer below. true false

decide whether the following statement is true or false. the cube function is odd and is increasing on the interval (-∞,∞). choose the correct answer below. true false

Answer

Explanation:

Step1: Define the cube function

The cube function is (y = f(x)=x^{3}).

Step2: Check if it's odd

We check if (f(-x)=-f(x)). Substitute (-x) into (f(x)): (f(-x)=(-x)^{3}=-x^{3}=-f(x)), so it's odd.

Step3: Check its monotonicity

Take the derivative (y' = f'(x)=3x^{2}\geq0) for all (x\in(-\infty,\infty)), and (y' = 0) only at (x = 0). The function is increasing on ((-\infty,\infty)).

Answer:

True