https://file.aiquickdraw.com/mathbot/file/1726753592534de5y4g5e.jpg

(f+g)(4) is ?
(g-f)(3) is ?
(g.f)(1) is ?
(f/g)(-1) is ?
(g(open dot)f)(0) is?
g(f(4)) is ?

Let's interpret the graph to answer your questions based on the functions \( f(x) \) and \( g(x) \) from the graph.

1. **\( (f + g)(4) \)**:  
   - First, find \( f(4) \) and \( g(4) \) from the graph.
   - \( f(4) = 0 \) (blue point at \( (4, 0) \)).
   - \( g(4) = 2 \) (purple point at \( (4, 2) \)).
   \[
   (f + g)(4) = f(4) + g(4) = 0 + 2 = 2.
   \]

2. **\( (g - f)(3) \)**:  
   - Find \( g(3) \) and \( f(3) \) from the graph.
   - \( g(3) = 2 \) (purple point at \( (3, 2) \)).
   - \( f(3) = 2 \) (blue point at \( (3, 2) \)).
   \[
   (g - f)(3) = g(3) - f(3) = 2 - 2 = 0.
   \]

3. **\( (g \cdot f)(1) \)**:  
   - Find \( g(1) \) and \( f(1) \) from the graph.
   - \( g(1) = 2 \) (purple point at \( (1, 2) \)).
   - \( f(1) = 3 \) (blue point at \( (1, 3) \)).
   \[
   (g \cdot f)(1) = g(1) \cdot f(1) = 2 \cdot 3 = 6.
   \]

4. **\( \left(\frac{f}{g}\right)(-1) \)**:  
   - Find \( f(-1) \) and \( g(-1) \) from the graph.
   - \( f(-1) = 3 \) (blue point at \( (-1, 3) \)).
   - \( g(-1) = 2 \) (purple point at \( (-1, 2) \)).
   \[
   \left(\frac{f}{g}\right)(-1) = \frac{f(-1)}{g(-1)} = \frac{3}{2}.
   \]

5. **\( g(f(0)) \)** (also written as \( g \circ f (0) \)):  
   - First, find \( f(0) \), then use this to find \( g(f(0)) \).
   - \( f(0) = 3 \) (blue point at \( (0, 3) \)).
   - Now, find \( g(3) = 2 \) (purple point at \( (3, 2) \)).
   \[
   g(f(0)) = g(3) = 2.
   \]

6. **\( g(f(4)) \)**:  
   - First, find \( f(4) \), then use this to find \( g(f(4)) \).
   - \( f(4) = 0 \) (blue point at \( (4, 0) \)).
   - Now, find \( g(0) = 2 \) (purple point at \( (0, 2) \)).
   \[
   g(f(4)) = g(0) = 2.
   \]

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Would you like more details or have further questions? Here are some related questions:

1. What is \( f(g(2)) \)?
2. How do we calculate \( (f - g)(0) \)?
3. What would \( (g \cdot f)(-2) \) be?
4. Find the value of \( \left(\frac{g}{f}\right)(2) \).
5. Determine the domain of the combined function \( (f + g)(x) \).

**Tip**: When working with composite functions like \( g(f(x)) \), always calculate the inner function first and then apply the result to the outer function.

(f+g)(4) is ? (g-f)(3) is ? (g.f)(1) is ? (f/g)(-1) is ? g(open dot)f)(0) is? g(f(4)) is ?

Learn how to solve function operations such as addition, subtraction, multiplication, division, and composite functions using graphs of f(x) and g(x). Evaluate (f+g)(4), (g-f)(3), (g.f)(1), and more. Suitable for students in Grades 10-12.

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