91Ó°ÊÓ

Rewrite the expression \(a^{-s / t}\) in radical form. Then state the index of the radical.

COMPLETE THE SENTENCE Square root functions and cube root functions are examples of __________ functions.

Let \(f\) and \(g\) be any two functions. Describe how you can use \(f, g\), and the four basic operations to create new functions.

WRITING How do you know when a radical expression is in simplest form?

Explain how to use the sign of \(a\) to determine the number of real fourth roots of \(a\) and the number of real fifth roots of \(a\).

\(f(x)=\sqrt{x+3}\)

Find \((f+g)(x)\) and \((f-g)(x)\) and state the domain of each. Then evaluate \(f+g\) and \(f-g\) for the given value of \(x\). $$ f(x)=\sqrt[3]{2 x}, g(x)=-11 \sqrt[3]{2 x} ; x=-4 $$

In Exercises 5-12, solve \(y=f(x)\) for \(x\). Then find the input(s) when the output is \(-3\). (See Example 1.) $$ f(x)=-7 x-2 $$

In Exercises 5-12, solve \(y=f(x)\) for \(x\). Then find the input(s) when the output is \(-3\). (See Example 1.) $$ f(x)=3 x^3 $$

Find \((f g)(x)\) and \(\left(\frac{f}{g}\right)(x)\) and state the domain of each. Then evaluate \(f g\) and \(\frac{f}{g}\) for the given value of \(x\). $$ f(x)=11 x^3, g(x)=7 x^{7 / 3} ; x=-8 $$