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The graphs of the functions f(x) and g(x) are shown. a) Find (f ∘ g)(1).

To solve \( (f \circ g)(1) \), we need to evaluate \( f(g(1)) \). This process involves two steps:

1. **Find \( g(1) \):**
   - Locate \( x = 1 \) on the graph and identify the corresponding \( y \)-value for the function \( g(x) \), which is the blue line.
   - From the graph, at \( x = 1 \), the value of \( g(1) \) appears to be \( y = 0 \).

2. **Find \( f(g(1)) = f(0) \):**
   - Now, use the result \( g(1) = 0 \) and find the corresponding \( y \)-value on the graph of the function \( f(x) \), which is the red curve.
   - From the graph, at \( x = 0 \), the value of \( f(0) \) is \( y = 1 \).

Thus, \( (f \circ g)(1) = f(g(1)) = f(0) = 1 \).

Would you like more details or have any questions?

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Here are some related questions you might find helpful:

1. How do you determine the domain of the composition of two functions?
2. What does the notation \( (f \circ g)(x) \) mean conceptually?
3. How can you determine the intersection points of two graphs algebraically?
4. What is the significance of finding \( f(g(x)) \) in real-world applications?
5. How would you compute the derivative of a composition of functions, such as \( (f \circ g)(x) \)?

**Tip:** When working with composite functions, always remember to evaluate the inner function first before applying the outer function.

Learn how to find (f ∘ g)(1) by evaluating composite functions f and g at x = 1. Step-by-step solution with graph analysis included. Suitable for high school students studying composite functions in mathematics.

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