Consider the set of ordered pairs. Verify if it is one-to-one. If so, find its inverse.
$g=\left\{\right(1,\frac{3}{2}),(4,\frac{5}{3}),(7,\frac{9}{4}),(10,\frac{11}{6}\left)\right\}$

• A. $g^{-1}={\left\lbrace(1,\frac23),\left(\frac14,\frac35\right),(\frac17,\frac49),(\frac{1}{10},\frac{6}{11})\right\rbrace}$
• B. $g^{-1}=\left\{\right(\frac{2}{3},1),(\frac{3}{5},\frac{1}{4}),(\frac{4}{9},\frac{1}{7}),(\frac{6}{11},\frac{1}{10}\left)\right\}$
• C. $g^{-1}=\left\{\right(\frac{3}{2},1),(\frac{5}{3},4),(\frac{9}{4},7),(\frac{11}{6},10\left)\right\}$
• D. The function is not one-to-one.

Answer: (C)

Verified step by step guidance

1. Identify the function for which you want to find the inverse. Let's denote the original function as \(f(x)\).
2. Replace \(f(x)\) with \(y\) to make the equation easier to work with: write \(y = f(x)\).
3. Swap the variables \(x\) and \(y\) in the equation. This means you rewrite the equation as \(x = f(y)\), which is the key step in finding the inverse function.
4. Solve the new equation for \(y\) in terms of \(x\). This involves algebraic manipulation such as isolating \(y\) on one side of the equation.
5. Once you have \(y\) expressed as a function of \(x\), rewrite it as \(f^{-1}(x)\), which represents the inverse function.