Math Problem Statement

Answer the next three questions based on the table.

Solution

Let's go through the two questions based on the table provided:

Table:

xxf(x)f(x)
36
5-6
-63
-35

Question 6: Evaluate f(5)f(5)

  • Find the value of f(x)f(x) when x=5x = 5.
    • From the table, when x=5x = 5, f(5)=6f(5) = -6.

Answer for Question 6:
f(5)=6f(5) = -6


Question 7: Solve f(x)=3f(x) = 3

  • Find the value(s) of xx for which f(x)=3f(x) = 3.
    • From the table, f(x)=3f(x) = 3 when x=6x = -6.

Answer for Question 7:
x=6x = -6


Let me know if this makes sense or if you have further questions! Here are some related questions to think about:

  1. What would f(3)f(3) be according to the table?
  2. How many values of xx are there for which f(x)=5f(x) = 5?
  3. If the function were linear, what would be its equation based on two points?
  4. What is the inverse of the function if we switch xx and f(x)f(x)?
  5. Can this function be classified as one-to-one?

Tip: When evaluating functions from a table, carefully match the input xx with its corresponding output to avoid mistakes.

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Math Problem Analysis

Mathematical Concepts

Function Evaluation
Inverse Functions

Formulas

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Theorems

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Suitable Grade Level

Grades 8-10