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!