Math Problem Statement

If g(x) is a one-to-one function, what is the value of g^(-1)(2)?

Solution

To find the value of g1(2)g^{-1}(2), we need to identify where g(x)=2g(x) = 2 in the given table. Since g1(y)g^{-1}(y) represents the value of xx such that g(x)=yg(x) = y, we search the table for the input that corresponds to the output of 2.

Looking at the table:

\hline x & g(x) \\ \hline -3 & -54 \\ -2 & -16 \\ -1 & -2 \\ 0 & 0 \\ 1 & 2 \\ 2 & 16 \\ 3 & 54 \\ \hline \end{array}$$ We see that $$g(1) = 2$$. Therefore: $$g^{-1}(2) = 1$$ Would you like any further details on this, or have any additional questions? Here are 5 related questions: 1. How do you verify if a function is one-to-one? 2. What is the difference between an inverse function and a reciprocal? 3. How do you graph the inverse of a function? 4. Can a function have more than one inverse? 5. How do you find the inverse of a function algebraically? **Tip**: To check if a function is one-to-one, use the horizontal line test on its graph—if no horizontal line intersects the graph more than once, the function is one-to-one.

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Math Problem Analysis

Mathematical Concepts

Functions
Inverse Functions
One-to-One Functions

Formulas

g(x) = y, g^(-1)(y) = x

Theorems

Definition of One-to-One Function
Inverse Function Theorem

Suitable Grade Level

Grades 9-11