Question

Find the domain of this without using the graphical method

Answer 1

By definition, the domain of a function is the complete set of possible values of the independent variable (x, usually).

We must find the domain of the following function:

`f(x)=\sqrt[5]{x^2-7x+2}\text{.}`

We see that the function is the odd root of a polynomial. Odd roots are defined for all real numbers, so this function is defined for all real numbers. The domain of the function is:

`\text{Domain }=(-\infty,\infty).`

Answer

`\text{Domain }=(-\infty,\infty).`