f (x) = x+1
g (x) = x²-2x+2
Find:
f•g (x) =

To find \( f \circ g (x) \) (also written as \( f(g(x)) \)), we need to substitute the expression for \( g(x) \) into the function \( f \).

Given:
\[ f(x) = x + 1 \]
\[ g(x) = x^2 - 2x + 2 \]

To find \( f(g(x)) \):
1. Substitute \( g(x) \) into \( f(x) \):
\[ f(g(x)) = f(x^2 - 2x + 2) \]

2. Since \( f(x) = x + 1 \), replace \( x \) in \( f(x) \) with \( g(x) \):
\[ f(x^2 - 2x + 2) = (x^2 - 2x + 2) + 1 \]

3. Simplify the expression:
\[ f(x^2 - 2x + 2) = x^2 - 2x + 2 + 1 \]
\[ f(x^2 - 2x + 2) = x^2 - 2x + 3 \]

Therefore:
\[ f \circ g (x) = x^2 - 2x + 3 \]

Do you want details or have any questions?

Here are some related questions:

1. How do you find the composition of two functions in general?
2. What is the domain of \( f \circ g(x) \)?
3. Can you find \( g \circ f(x) \) given the same functions \( f \) and \( g \)?
4. What is the graphical interpretation of function composition?
5. How does the composition of functions affect their range?
6. What are the properties of composite functions?
7. How would you determine if \( f \circ g \) is one-to-one?
8. Can you determine if \( f \circ g \) is onto?

**Tip:** When working with function composition, always ensure that the range of the inner function (in this case \( g(x) \)) falls within the domain of the outer function (in this case \( f(x) \)).

Learn how to calculate the composition of functions f and g, where f(x) = x + 1 and g(x) = x^2 - 2x + 2. Understand the step-by-step process to find f • g (x). Suitable for students in Grades 10-12.

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