91Ó°ÊÓ

Simplify each expression. Assume that all variables are positive. $$\left[\left(\sqrt{x^{3} y^{3}}\right)^{\frac{1}{3}}\right]^{-1}$$

Evaluate each expression. \(_{7} \mathrm{P}_{3}\)

Solve each equation. $$ 81 x^{4}-1=0 $$

Grades Suppose your teacher offers to give the whole class a bonus if everyone passes the next math test. The teacher says she will \((1)\) give everyone a 10 -point bonus and \((2)\) increase everyone's grade by 9\(\%\) of their score. a. Let \(x\) represent the original test scores. Write statements \((1)\) and \((2)\) as the functions \(f(x)\) and \(g(x),\) respectively. b. Explain the meaning of \(f(g(x))\) . Evaluate \(f(g(75))\) . c. Explain the meaning of \(g(f(x)) .\) Evaluate \(g(f(75))\) . d. Does \(g(f(x))=f(g(x)) ?\)

Compare the domains and ranges of the functions \(f(x)=\sqrt{x-1}\) and \(g(x)=\sqrt{x}-1\)

Simplify each radical expression. Use absolute value symbols as needed. $$ \sqrt{121 a^{90}} $$

Find the inverse of each function. Is the inverse a function? \(f(x)=4 x-1\)

Writing Explain why \((-64)^{\frac{1}{3}}=-64^{\frac{1}{3}}\) and \((-64)^{\frac{1}{2}} \neq-64^{\frac{1}{2}}\).

Simplify each radical expression. Use absolute value symbols as needed. $$ -\sqrt{81 c^{48} d^{64}} $$

Let \(f(x)=3 x-2\) and \(g(x)=x^{2}+1 .\) Perform each function operation and use the properties of real numbers to justify each step in simplifying your answer. $$ f(x) \cdot g(x) $$