Question

1. a table of selected values is given for a one - to - one function, g. what is $g^{-1}(1)$?

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$$\begin{array}{c|cccccc}x&-4&-2&0&1&5&8\\\\g(x)&10&8&-3&-1&-4&1\\end{array}$$

Explanation:

Step1: Recall inverse function definition

For a one - to - one function \(y = g(x)\), the inverse function \(g^{-1}(y)\) gives the value of \(x\) such that \(g(x)=y\). So, to find \(g^{-1}(1)\), we need to find the value of \(x\) for which \(g(x) = 1\).

Step2: Look at the table

The table has values of \(x\) and corresponding \(g(x)\) values. We look for the row where \(g(x)=1\). From the table, when \(x = 8\), \(g(x)=1\).

Answer:

\(8\)