91Ó°ÊÓ

change each repeating decimal to a ratio of two integers. $$ 0.199999 \ldots $$

Find a formula for \(f^{-1}(x)\) and then verify that \(f^{-1}(f(x))=x\) and \(f\left(f^{-1}(x)\right)=x\) $$ f(x)=\frac{x-1}{x+1} $$

. Find the distance between the points on the circle \(x^{2}+2 x+y^{2}-2 y=20\) with the \(x\) -coordinates \(-2\) and 2. How many such distances are there?

Find the solution sets of the given inequalities. $$ |5 x-6|>1 $$

change each repeating decimal to a ratio of two integers. $$ 0.399999 \ldots $$

Find the value of \(k\) such that the line \(k x-3 y=10\) (a) is parallel to the line \(y=2 x+4\); (b) is perpendicular to the line \(y=2 x+4\); (c) is perpendicular to the line \(2 x+3 y=6\).

Find a formula for \(f^{-1}(x)\) and then verify that \(f^{-1}(f(x))=x\) and \(f\left(f^{-1}(x)\right)=x\) $$ f(x)=\left(\frac{x-1}{x+1}\right)^{3} $$

Find the solution sets of the given inequalities. $$ |2 x-7|>3 $$

Which of the following functions satisfies \(f(x+y)=f(x)+f(y)\) for all real numbers \(x\) and \(y\) ? (a) \(f(t)=2 t\) (b) \(f(t)=t^{2}\) (c) \(f(t)=2 t+1\) (d) \(f(t)=-3 t\)

Let \(f(x+y)=f(x)+f(y)\) for all \(x\) and \(y\). Prove that there is a number \(m\) such that \(f(t)=m t\) for all rational numbers t. Hint: First decide what \(m\) has to be. Then proceed in steps, starting with \(f(0)=0, f(p)=m p\) for a natural number \(p\), \(f(1 / p)=m / p\), and so on.