Find (f o g) (x) from f(x) = x + 2  and g(x) 2x - 1

We are given two functions:

- \( f(x) = x + 2 \)
- \( g(x) = 2x - 1 \)

To find \( (f \circ g)(x) \), which represents the composition of functions \( f \) and \( g \), we substitute \( g(x) \) into \( f(x) \).

So,

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

First, substitute \( g(x) = 2x - 1 \) into \( f(x) \):

\[
f(g(x)) = f(2x - 1)
\]

Now apply \( f(x) = x + 2 \) to \( 2x - 1 \):

\[
f(2x - 1) = (2x - 1) + 2 = 2x + 1
\]

Thus,

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

Would you like more details on this process or have any questions?

Here are some related questions to expand on this concept:

1. How do you find \( (g \circ f)(x) \) for these functions?
2. What is the general rule for composing two functions?
3. Can the composition of functions be reversed, and how does that affect the result?
4. How do you determine the domain of \( (f \circ g)(x) \)?
5. How does composition of functions relate to real-world applications?

**Tip:** When composing functions, always remember the order matters. You substitute the inside function into the outside one!

Find (f o g) (x) from f(x) = x + 2 and g(x) = 2x - 1

Learn how to find the composition of functions (f o g)(x) for f(x) = x + 2 and g(x) = 2x - 1. This detailed solution covers key algebraic concepts related to function composition, making it suitable for students in Grades 9-11.

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