Consider the set of ordered pairs. Verify if it is one-to-one. If so, find its inverse.
$f=\left\{\right(2,9),(4,11),(6,15),(8,20\left)\right\}$

• A. $f^{-1}=\left\{\right(\frac{1}{9},\frac{1}{2}),(\frac{1}{11},\frac{1}{4}),(\frac{1}{15},\frac{1}{6}),(\frac{1}{20},\frac{1}{8}\left)\right\}$
• B. $f^{-1}=\left\{\right(\frac{1}{2},\frac{1}{9}),(\frac{1}{4},\frac{1}{11}),(\frac{1}{6},\frac{1}{15}),(\frac{1}{8},\frac{1}{20}\left)\right\}$
• C. $f^{-1}=\left\{\right(9,2),(11,4),(15,6),(20,8\left)\right\}$
• D. The function is not one-to-one.

Answer: (C)

Verified step by step guidance

1. Understand that the problem is about finding the inverse of a function. The inverse function essentially reverses the effect of the original function, swapping inputs and outputs.
2. Start with the original function, which is usually given as \(y = f(x)\). If the function is not explicitly provided, identify it first from the problem statement.
3. To find the inverse, swap the variables \(x\) and \(y\) in the equation. This means you rewrite the equation as \(x = f(y)\).
4. Solve this 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 denotes the inverse function.