Evaluating Function Values from a Table: Solve f(6) and Solve f(z) = 1

Math Problem Statement

Evaluate f(6) from the given table and solve f(z) = 1.

From the image provided, we can see a table with values of $z$ and their corresponding $f(z)$ values. You are tasked with two things:

\hline z & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline f(z) & 32 & 38 & 10 & 72 & 62 & 63 & 49 & 41 \\ \hline \end{array}$$ ### Step 1: Evaluate $$f(6)$$ From the table, when $$z = 6$$, the value of $$f(z) = 49$$. So, $$f(6) = 49$$. ### Step 2: Solve $$f(z) = 1$$ We need to find the value of $$z$$ such that $$f(z) = 1$$. Looking at the table, none of the $$f(z)$$ values are equal to 1, so there is no solution for this part. Would you like further details or explanations on these steps? Here are a few related questions you could explore: 1. How would you calculate $$f(z)$$ if you were given an equation instead of a table? 2. What does it mean for a function to have no solution for a given $$f(z) = c$$? 3. Can a function have more than one solution for a given $$f(z) = c$$? 4. How could the function's behavior change if the table represented a quadratic or exponential function? 5. What if the data points were interpolated—how could we estimate $$f(6.5)$$? **Tip:** Always double-check function values in a table for specific inputs to avoid misinterpretation!

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Functions
Table Lookup

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