The composition of functions \( (g \circ f)(x) \) means you substitute the function \( f(x) \) into \( g(x) \).

Given:

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

Now, let's compute \( g(f(x)) \):

\[
(g \circ f)(x) = g(f(x)) = g(3x + 4)
\]

Substitute \( 3x + 4 \) into \( g(x) \):

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

Simplify:

\[
= 2(3x) + 2(4) - 3
\]
\[
= 6x + 8 - 3
\]
\[
= 6x + 5
\]

So, \( (g \circ f)(x) = 6x + 5 \).

Would you like further details or have any questions?

Here are 5 related questions to consider:

1. What is \( (f \circ g)(x) \)?
2. How would you solve \( (g \circ f)(2) \)?
3. If \( g(x) = x^2 - 1 \), how would that change \( (g \circ f)(x) \)?
4. What is the domain of \( g(f(x)) \)?
5. How does the order of function composition affect the result?

**Tip:** Always check the domain of the inner function when composing functions!

If f(x) = 3x + 4 and g(x) = 2x - 3, what is (g o f)(x)?

Learn how to compose two linear functions and solve (g o f)(x), where f(x) = 3x + 4 and g(x) = 2x - 3. This step-by-step guide covers function composition and key algebraic concepts. Ideal for students in Grades 9-11.

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