Math Problem Statement

Use the graphs of f(x) and g(x) to evaluate each of the following.

( f + g )(12) =

Solution

To evaluate (f+g)(12)(f + g)(12) using the graphs provided:

  1. Find f(12)f(12): From the graph of f(x)f(x), locate the value of f(x)f(x) when x=12x = 12.
  2. Find g(12)g(12): Similarly, from the graph of g(x)g(x), find the value of g(x)g(x) when x=12x = 12.
  3. Add the values: Finally, add f(12)f(12) and g(12)g(12) to get (f+g)(12)(f + g)(12).

Step-by-Step Solution:

  1. f(12)f(12):

    • From the graph of f(x)f(x), at x=12x = 12, the value of f(x)f(x) is 33.
  2. g(12)g(12):

    • From the graph of g(x)g(x), at x=12x = 12, the value of g(x)g(x) is 66.
  3. Calculate (f+g)(12)(f + g)(12): (f+g)(12)=f(12)+g(12)=3+6=9(f + g)(12) = f(12) + g(12) = 3 + 6 = 9

Thus, (f+g)(12)=9(f + g)(12) = 9.

Would you like more details or have any questions?

Here are 5 related questions to consider:

  1. What is (fg)(12)(f - g)(12)?
  2. How would you find (f×g)(12)(f \times g)(12)?
  3. What are the values of f(7)f(7) and g(7)g(7)?
  4. How do you find the point of intersection of f(x)f(x) and g(x)g(x)?
  5. What is the domain and range of f(x)f(x) and g(x)g(x)?

Tip: When working with functions graphically, always ensure you accurately read the values from the graph, paying close attention to the scales on the axes.

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Math Problem Analysis

Mathematical Concepts

Functions
Graphs
Addition of Functions

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12