To find the sum of the numeric values of the inverse of the function $f(x) = 2x + 1$, we first need to find the inverse function and then evaluate its numeric sum.

Step 1: Find the Inverse of $f(x)$

The function $f(x) = 2x + 1$ is a linear function. To find the inverse, we follow these steps:

1. Let $y = f(x)$, so: $y = 2x + 1$

2. Solve for $x$ in terms of $y$: $y - 1 = 2x$ $x = \frac{y - 1}{2}$

3. Now, replace $y$ with $x$ to get the inverse function: $f^{-1}(x) = \frac{x - 1}{2}$

Step 2: Sum of Numeric Values of the Inverse

The problem asks for the sum of numeric values of the inverse function. This is a bit ambiguous because there are infinite values for $x$, so the sum would be unbounded. However, if you're asking for the sum of a particular set of numeric values for the inverse, we would need to specify a set of inputs (e.g., values of $x$) to calculate the sum of their corresponding values under the inverse function.

If you want to find the sum of specific values of the inverse function (say for $x = 1, 2, 3, \dots$), please clarify which values you're referring to.

Would you like to proceed with a specific set of $x$-values for the inverse function, or do you need further clarification? Let me know!

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Related Questions:

1. How do we find the inverse of other types of functions, like quadratic functions?
2. What is the geometric interpretation of the inverse function?
3. How do we verify if two functions are true inverses of each other?
4. Can the inverse of a function always be found algebraically?
5. What happens if the function is not one-to-one (injective)? How does this affect the inverse?

Tip:

Remember, when finding the inverse of a function, always check if the function is one-to-one (injective). If a function is not one-to-one, it will not have an inverse that is also a function.