Question

8.7 use radicals in functions (homework)
score: 6/10 answered: 7/10
question 8
find the domain of $f(x)=sqrt7{16x^{2}-9}$.
the domain is $xin$ (enter your answer in interval notation)

Explanation:

Step1: Recall domain - rule for odd - root functions

For a function of the form $y = \sqrt[n]{u(x)}$, when $n$ is odd (here $n = 7$), the domain is all real numbers for which the expression inside the root $u(x)$ is well - defined. Since the expression inside the seventh - root is a polynomial $u(x)=16x^{2}-9$, and polynomials are defined for all real numbers, there are no restrictions based on the nature of the root.
The domain of the function $f(x)=\sqrt[7]{16x^{2}-9}$ is the set of all real numbers because we can take the seventh - root of any real number.

Answer:

$(-\infty,\infty)$