To find the composite function $(f \circ g)(x)$, you need to substitute $g(x)$ into $f(x)$. In other words, you evaluate $f$ at $g(x)$.

Given:

• $f(x) = 3x - 5$
• $g(x) = 2x + 1$

We want to find $f(g(x))$. This means substituting $g(x) = 2x + 1$ into $f(x)$:

$f(g(x)) = f(2x + 1)$

Now, replace $x$ in $f(x) = 3x - 5$ with $2x + 1$:

$f(2x + 1) = 3(2x + 1) - 5$

Distribute the 3:

$f(2x + 1) = 6x + 3 - 5$

Simplify:

$f(2x + 1) = 6x - 2$

So, the composite function $(f \circ g)(x)$ is:

$(f \circ g)(x) = 6x - 2$

Would you like more details on composite functions or have any other questions?

Here are 5 related questions to explore further:

1. What is the composite function $(g \circ f)(x)$?
2. How do you find the inverse of a composite function?
3. What happens if you compose more than two functions, like $(h \circ f \circ g)(x)$?
4. Can you graph composite functions and what do they look like?
5. How do you solve composite functions if the output is known (e.g., $(f \circ g)(x) = 10$)?

Tip: When working with composite functions, always follow the order of operations, starting from the inside function first.