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Magazine Problem 107
Use rational exponents to simplify. Do not use fraction exponents in the final answer. $$ (\sqrt[5]{a^{2} b^{4}})^{15} $$
Problem 107
Determine algebraically the domain of each function described. Then use a graphing calculator to confirm your answer and to estimate the range. $$ f(x)=1-\sqrt{x+1} $$
Problem 108
Let \(f(x)=x^{2} .\) Find each of the following. $$f(7+\sqrt{3})$$
Problem 108
Use rational exponents to simplify. Do not use fraction exponents in the final answer. $$ (\sqrt[3]{x^{2} y^{5}})^{12} $$
Problem 108
Determine algebraically the domain of each function described. Then use a graphing calculator to confirm your answer and to estimate the range. $$ g(x)=2+\sqrt{3 x-5} $$
Problem 109
The absolute value of a complex number \(a+b i\) is its distance from the origin. Using the distance formula, we have \(|a+b i|=\sqrt{a^{2}+b^{2}} .\) Find the absolute value of each complex number. $$ |3+4 i| $$
Problem 109
Determine algebraically the domain of each function described. Then use a graphing calculator to confirm your answer and to estimate the range. $$ g(x)=3+\sqrt{x^{2}+4} $$
Problem 109
Use rational exponents to simplify. Do not use fraction exponents in the final answer. $$ \sqrt[3]{\sqrt[4]{x y}} $$
Problem 109
Let \(f(x)=x^{2} .\) Find each of the following. $$f(\sqrt{3}-\sqrt{5})$$
Problem 110
Determine algebraically the domain of each function described. Then use a graphing calculator to confirm your answer and to estimate the range. $$ f(x)=5-\sqrt{3 x^{2}+1} $$
