Chapter 7

If \((f \circ g)(x)=x^{2}-6 x+8\) and \(g(x)=x-3,\) which expression could represent \(f(x) ?\) $$\begin{array}{llll}{\text { F. } x-4} & {\text { G. } x-1} & {\text { H. } x^{2}-1} & {\text { J. } x^{2}-6 x+5}\end{array}$$

Solve each equation by factoring. \(3 x^{2}+8 x+4=0\)

Which expression is NOT equivalent to \(\sqrt[4]{4 n^{2}} ?\) \(\begin{array}{llll}{\text { A. }\left(4 n^{2}\right)^{\frac{1}{4}}} & {\text { B. } 2 n^{\frac{1}{2}}} & {\text { C. }(2 n)^{\frac{1}{2}}} & {\text { D. } \sqrt{2 n}}\end{array}\)

Solve using the Quadratic Formula. \(x^{2}-9 x+15=0\)

List all possible rational roots for each equation. Then use the Rational Root Theorem to find each root. $$ 3 x^{3}-5 x^{2}-4 x+4=0 $$

Let \(g(x)=x-3\) and \(h(x)=x^{2}+6 .\) Find \((h \circ g)(1)\) $$\begin{array}{llll}{\text { A. }-14} & {\text { B. } 4} & {\text { C. } 5} & {\text { D. } 10}\end{array}$$

Solve each equation by factoring. \(9 x^{2}+15 x+4=0\)

Which expression is NOT equivalent to \(\sqrt[6]{81 x^{4} y^{8}} ?\) \(\begin{array}{llll}{\text { E. }\left(3 x y^{2}\right)^{\frac{2}{3}}} & {\text { G. }(3 x)^{\frac{3}{3}} y^{\frac{4}{3}}} & {\text { H. }\left(3 x^{2} y^{4}\right)^{\frac{1}{3}}} & {\text { 1. } \sqrt[3]{9 x^{2} y^{4}}}\end{array}\)

Solve using the Quadratic Formula. \(x^{2}+10 x+11=0\)

List all possible rational roots for each equation. Then use the Rational Root Theorem to find each root. $$ 3 x^{3}+10 x^{2}-x-12=0 $$

If \(f(x)=3-x\) and \(g(x)=x^{2}-3,\) which expression has the greatest value? $$\begin{array}{llll}{\text { F. }(g \circ f)(-3)} & {\text { G. }(f \circ g)(-3)} & {\text { H. }(f \cdot g)(-3)} & {\text { J. }(g-f)(-3)}\end{array}$$

Solve each equation by factoring. \(4 x^{2}+11 x+6=0\)

Which equation represents a property of exponents? \(\begin{array}{llll}{\text { A. }\left(a^{m}\right)^{n}=a^{m+n}} & {\text { B. }\left(\frac{a}{b}\right)^{m}=\frac{a^{m}}{b}} & {\text { C. } a^{-m}=\frac{1}{a^{m}}} & {\text { D. } a^{m} \cdot a^{n}=a^{m n}}\end{array}\)

Solve using the Quadratic Formula. \(x^{2}-12 x+25=0\)

List all possible rational roots for each equation. Then use the Rational Root Theorem to find each root. $$ 2 x^{3}-11 x^{2}-x+30=0 $$

If \(f(x)=x^{2}\) and \(g(x)=x-1,\) which statement is true? A. \((f \circ g)(x) \geq(g \circ f)(x)\) for all values of \(x .\) B. \((f \circ g)(x) \leq(g \circ f)(x)\) for all values of \(x\) . C. \((f \circ g)(x)=(g \circ f)(x)\) only for \(x=1\) D. \((f \circ g)(x) \neq(g \circ f)(x)\) for any value of \(x .\)

Which expression is equivalent to \(\left(\frac{1}{64}\right)^{-\frac{1}{6}} ?\) \(\mathrm{F}\left(\frac{1}{2}\right)^{-6} \quad\) G. \(4^{3} \quad\) H. 2\(\quad J.64^{6}\)

Solve using the Quadratic Formula. \(8 x^{2}+2 x-15=0\)

List all possible rational roots for each equation. Then use the Rational Root Theorem to find each root. $$ x^{3}-6 x^{2}+11 x-6=0 $$

Which expression is equivalent to \(\left(n^{\frac{3}{2}} \div n^{-\frac{1}{6}}\right)^{-3} ?\) \(\begin{array}{llll}{\text { A. } n^{27}} & {\text { B. } n^{-27}} & {\text { C. } n^{-4}} & {\text { D. } n^{-5}}\end{array}\)

List all possible rational roots for each equation. Then use the Rational Root Theorem to find each root. $$ x^{3}+3 x^{2}-4 x-12=0 $$

Let \(g(x)=x^{2}-4\) and \(h(x)=4 x-6 .\) Find \(\left(\frac{g}{h}\right)(x)\)

Which number is closest to \(\left(81 n^{2}\right)^{0.75}\) for \(n=2 ?\) \(\begin{array}{llll}{\text { E. } 45.4} & {\text { G. } 76.4} & {\text { H. } 243.0} & {\text { 1.2061.9 }}\end{array}\)

If \(f(x)=3 x-4\) and \(g(x)=x+3,\) what does \((f \cdot g)(x)\) mean? What is \((f \cdot g)(x) ?\) Simplify the answer.

What is the value of \(x\) if \(32^{0.8} x=1 ?\) Simplify the answer.

Solve. Check for extraneous solutions. $$ \sqrt{x^{2}+3}=x+1 $$

For \(x>0\) and \(y>0,\) write \(\sqrt{9 x^{5} y^{-6}}\) in simplest form.

Solve. Check for extraneous solutions. $$ x+8=\left(x^{2}+16\right)^{\frac{1}{2}} $$

Find a nonzero number \(q\) such that \(q(1-\sqrt{2})\) is a rational number. Explain.

Solve. Check for extraneous solutions. $$ \sqrt{x^{2}+9}=x+1 $$

Simplify. Rationalize all denominators. $$6 \sqrt[3]{3}-2 \sqrt[3]{3}$$

Solve. Check for extraneous solutions. $$ \left(x^{2}-9\right)^{\frac{1}{2}}-x=-3 $$

Simplify. Rationalize all denominators. $$ 3 \sqrt{18}+2 \sqrt{72} $$

Solve. Check for extraneous solutions. $$ \sqrt{x^{2}+12}-2=x $$

Simplify. Rationalize all denominators. $$ (\sqrt{5}-1)(\sqrt{5}+4) $$

Solve. Check for extraneous solutions. $$ (3 x)^{\frac{1}{2}}=(x+6)^{\frac{1}{2}} $$

Simplify. Rationalize all denominators. $$ (\sqrt{8}-\sqrt{7})^{2} $$

Expand each binomial. $$ (x+4)^{8} $$

Simplify. Rationalize all denominators. $$ \frac{2+\sqrt{10}}{2-3 \sqrt{5}} $$

Expand each binomial. $$ (x+y)^{6} $$

Simplify. Rationalize all denominators. $$ \frac{-2+\sqrt{8}}{-3-\sqrt{2}} $$

Expand each binomial. $$ (2 x-y)^{4} $$

Factor each expression. $$ 4 x^{3}-8 x^{2}+16 x $$

Expand each binomial. $$ (2 x-3 y)^{7} $$

Factor each expression. $$ x^{2}+4 x+4 $$

Expand each binomial. $$ (9-2 x)^{5} $$

Factor each expression. $$ x^{2}-18 x+81 $$

Expand each binomial. $$ (4 x-y)^{5} $$

Factor each expression. $$ 16 a^{2}-9 b^{2} $$

Expand each binomial. $$ \left(x^{2}+x\right)^{4} $$