what is the formula of composition function 

The composition of functions involves applying one function to the result of another function. If you have two functions, say \( f(x) \) and \( g(x) \), the composition of these two functions is written as:

\[
(f \circ g)(x) = f(g(x))
\]

This means that you first apply the function \( g \) to the input \( x \), and then apply the function \( f \) to the result of \( g(x) \).

### Steps for Composing Functions:
1. **Start with an input** \( x \).
2. **Apply** \( g(x) \).
3. **Apply** \( f \) to the result of \( g(x) \), which gives \( f(g(x)) \).

### Example:

Let \( f(x) = 2x + 1 \) and \( g(x) = x^2 \). The composition \( (f \circ g)(x) \) is:

\[
(f \circ g)(x) = f(g(x)) = f(x^2) = 2(x^2) + 1 = 2x^2 + 1
\]

Would you like more examples or further explanation?

### 5 Related Questions:
1. How do you compose three functions, say \( f(x) \), \( g(x) \), and \( h(x) \)?
2. What is the difference between \( f(g(x)) \) and \( g(f(x)) \)?
3. Can all functions be composed with each other?
4. How do you find the domain of a composite function?
5. What is the inverse of a composite function?

### Tip: 
Always check the domain of both functions when composing, as the domain of the composition may be restricted based on the inner function.

what is the formula of composition function

Learn how to compose functions using the formula (f ∘ g)(x) = f(g(x)). This concept applies to algebra and introduces key ideas such as applying one function to the result of another. Suitable for high school students, Grades 10-12.

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