91Ó°ÊÓ

Solve for \(x\) without using a calculating utility. \(\log _{10}(\sqrt{x})=-1\)

Sketch the graph of the equation by making appropriate transformations to the graph of a basic power function. If you have a graphing utility, use it to check your work. (a) \(y=1-\sqrt{x+2}\) (b) \(y=1-\sqrt[3]{x+2}\) (c) \(y=\frac{5}{(1-x)^{3}}\) (d) \(y=\frac{2}{(4+x)^{4}}\)

Find a formula for \(f^{-1}(x)\), and state the domain of the function \(f^{-1}\). \(f(x)=\sqrt{x+3}\)

Solve for \(x\) without using a calculating utility. \(\ln \left(x^{2}\right)=4\)

Sketch the graph of the equation by translating, reflecting, compressing, and stretching the graph of \(y=x^{2}, y=\sqrt{x}\), \(y=1 / x, y=|x|\), or \(y=\sqrt[3]{x}\) appropriately. Then use a graphing utility to confirm that your sketch is correct. $$ y=1-|x-3| $$

Find a formula for \(f^{-1}(x)\), and state the domain of the function \(f^{-1}\). \(f(x)=-\sqrt{3-2 x}\)

Sketch the graph of \(y=x^{2}+2 x\) by completing the square and making appropriate transformations to the graph of \(y=x^{2}\)

Sketch the graph of the equation by translating, reflecting, compressing, and stretching the graph of \(y=x^{2}, y=\sqrt{x}\), \(y=1 / x, y=|x|\), or \(y=\sqrt[3]{x}\) appropriately. Then use a graphing utility to confirm that your sketch is correct. $$ y=|2 x-1|+1 $$

Solve for \(x\) without using a calculating utility. \(\ln (1 / x)=-2\)

Determine whether the statement is true or false. Explain your answer. A curve that crosses the \(x\) -axis at two different points cannot be the graph of a function.