To solve $(f \circ g)(3)$, we need to evaluate the composition of two functions $f(x)$ and $g(x)$ at $x = 3$. However, you've provided the function $f(x) = 4x + 3$ and a partial expression $q(x) - 2 - 3x$ which seems like an incomplete or typo for the second function.

Let me assume you meant $g(x) = 2 - 3x$ as the second function. If this is the correct interpretation, we'll proceed as follows:

Step-by-step Solution:

1. Define the functions:

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

2. Find $g(3)$:

   Substitute $x = 3$ into $g(x)$: $g(3) = 2 - 3(3)$ $g(3) = 2 - 9$ $g(3) = -7$

3. Find $(f \circ g)(3)$:

   $(f \circ g)(3) = f(g(3))$. We already know $g(3) = -7$.

   Now, substitute $g(3) = -7$ into $f(x)$: $f(g(3)) = f(-7)$ $f(-7) = 4(-7) + 3$ $f(-7) = -28 + 3$ $f(-7) = -25$

Conclusion:

$(f \circ g)(3) = -25$

Would you like more details or have any questions about this solution?

Related Questions:

1. What is $(g \circ f)(3)$ given the functions above?
2. How do you find the inverse of $f(x) = 4x + 3$?
3. What is the domain and range of $f(x)$ and $g(x)$?
4. How would you graph the functions $f(x)$ and $g(x)$?
5. What is the result of $(f \circ f)(x)$ for any $x$?

Tip:

When solving function compositions, always evaluate the inner function first, then use its result to compute the outer function.