91Ó°ÊÓ

For each function as defined that is one-to-one, (a) write an equation for the inverse function in the form y = Æ’ -11x2, (b) graph Æ’ and Æ’ -1 on the same axes, and (c) give the domain and the range of Æ’ and Æ’ -1. If the function is not one-to-one, say so. $$f(x)=\frac{x+2}{x-1}, \quad x \neq 1$$

Solve each rational inequality. Write each solution set in interval notation. $$\frac{6-x}{x+2}>1$$

Solve each equation for the indicated variable. Assume no denominators are \(0 .\) $$\mathscr{A}=\pi r^{2}, \quad \text { for } r$$

Solve each equation. $$(2 x-1)^{2 / 3}=x^{1 / 3}$$

Find each quotient. Write the answer in standard form \(a+b i .\) $$\frac{1-3 i}{1+i}$$

For each function as defined that is one-to-one, (a) write an equation for the inverse function in the form y = Æ’ -11x2, (b) graph Æ’ and Æ’ -1 on the same axes, and (c) give the domain and the range of Æ’ and Æ’ -1. If the function is not one-to-one, say so. $$f(x)=\frac{-3 x+12}{x-6}, \quad x \neq 6$$

Solve each equation for the indicated variable. Assume no denominators are \(0 .\) $$F=\frac{k M v^{2}}{r}, \quad \text { for } v$$

Solve each rational inequality. Write each solution set in interval notation. $$\frac{3}{x-6} \leq 2$$

Solve each equation. $$(x-3)^{2 / 5}=(4 x)^{1 / 5}$$

Solve each equation for the indicated variable. Assume no denominators are \(0 .\) $$E=\frac{e^{2} k}{2 r}, \quad \text { for } e$$