To find $(f \circ g)(x)$, we need to evaluate $f(g(x))$, which means substituting $g(x)$ into the function $f(x)$.

Given:

• $f(x) = 3x$
• $g(x) = 4x^2 - 5x + 1$

Steps:

1. Start with the expression for $f(x)$:
   $f(x) = 3x$

2. Now, substitute $g(x)$ into $f(x)$:
   $f(g(x)) = 3(g(x)) = 3(4x^2 - 5x + 1)$

3. Distribute the 3 to each term inside the parentheses: $f(g(x)) = 3(4x^2) + 3(-5x) + 3(1)$ $f(g(x)) = 12x^2 - 15x + 3$

So, $(f \circ g)(x) = 12x^2 - 15x + 3$.

Would you like further details or clarification on any part?

Here are 5 related questions:

1. How do you find $(g \circ f)(x)$ with these functions?
2. What happens if you swap the order of composition in functions?
3. Can you differentiate $(f \circ g)(x)$?
4. What are the domains of $f(x)$, $g(x)$, and $(f \circ g)(x)$?
5. How do you determine whether a composition of functions is one-to-one?

Tip: Always make sure to substitute the entire function when performing composition, including all terms.