Chapter 3.2, Problem 6QR

To determine

To calculate: The domain of the function $y$ .

Answer to Problem 6QR

The required domain of $y$ is. $\left(-\infty ,+\infty \right)$

Explanation of Solution

Given Information:

The algebraic function is:

  $y=x^{4/3}$

Calculation:

The given algebraic function is: $y=x^{4/3}$

Find the domain of the above function.

The given function can be written as $y=\sqrt[3]{x^4}$ .

Since, the given function is a cube root which is nothing but an odd numbered root and there is no limit as the domain.

Thus the exponent $x^4$ is defined for all real numbers as well, y is defined for all real.

Hence, the required domain of function $y$ is $\left(-\infty ,+\infty \right)$ .