91Ó°ÊÓ

Find a formula for the inverse function \(f^{-1}\) of the indicated function \(f\). $$ f(x)=4 x^{3 / 7}-1 $$

Find six distinct points whose distance from the origin equals 3 .

Find a formula for the inverse function \(f^{-1}\) of the indicated function \(f\). $$ f(x)=7+8 x^{5 / 9} $$

Sketch the graph of the given function \(f\) on the domain \(\left[-3,-\frac{1}{3}\right] \cup\left[\frac{1}{3}, 3\right]\). $$ f(x)=\frac{1}{x}+1 $$

Suppose \(a>b>0\). Find a formula in terms of \(x\) for the distance from a typical point \((x, y)\) on the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) to the point \(\left(\sqrt{a^{2}-b^{2}}, 0\right) .\)

Sketch the graph of the given function \(f\) on the domain \(\left[-3,-\frac{1}{3}\right] \cup\left[\frac{1}{3}, 3\right]\). $$ f(x)=\frac{1}{x^{2}}+2 $$

Suppose \(a>b>0\). Find a formula in terms of \(x\) for the distance from a typical point \((x, y)\) on the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) to the point \(\left(-\sqrt{a^{2}-b^{2}}, 0\right)\)

Sketch the graph of the given function \(f\) on the domain \(\left[-3,-\frac{1}{3}\right] \cup\left[\frac{1}{3}, 3\right]\). $$ f(x)=\frac{1}{x^{2}}-2 $$

Suppose \(b>a>0\). Find a formula in terms of \(y\) for the distance from a typical point \((x, y)\) on the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) to the point \(\left(0, \sqrt{b^{2}-a^{2}}\right)\).

Sketch the graph of the given function \(f\) on the domain \(\left[-3,-\frac{1}{3}\right] \cup\left[\frac{1}{3}, 3\right]\). $$ f(x)=\frac{1}{x}-3 $$