To find the composition of functions \((f \circ g)(x)\), we substitute the output of \(g(x)\) into the input of \(f(x)\). Given:

- \(f(x) = 3x + 4\)
- \(g(x) = 2x - 3\)

The composition \((f \circ g)(x)\) means \(f(g(x))\). Let's find this step-by-step:

1. **Substitute \(g(x)\) into \(f(x)\):**

\[
f(g(x)) = f(2x - 3)
\]

2. **Replace \(x\) in \(f(x)\) with \(2x - 3\):**

\[
f(2x - 3) = 3(2x - 3) + 4
\]

3. **Simplify the expression:**

\[
f(2x - 3) = 3 \cdot 2x - 3 \cdot 3 + 4
\]

\[
f(2x - 3) = 6x - 9 + 4
\]

\[
f(2x - 3) = 6x - 5
\]

So, the composition \((f \circ g)(x) = 6x - 5\).

Would you like more details or have any questions?

Here are 5 related questions that might interest you:

1. What is the composition \((g \circ f)(x)\) for the same functions?
2. How do you find the inverse of a function, and can you find the inverse of \(f(x) = 3x + 4\)?
3. What is the domain and range of the composition function \((f \circ g)(x)\)?
4. How do you determine if two functions are inverses of each other?
5. How does function composition relate to transformations in geometry?

**Tip:** When composing functions, always substitute the entire expression of the inner function into the variable of the outer function.

Learn how to find the composition of two functions (f o g) where f(x)=3x + 4 and g(x)=2x - 3. This step-by-step solution explores key algebraic concepts, including function composition, and is suitable for students in Grades 10-12.

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