Let's solve the given function composition problem step by step. The question asks to find $(f \circ g)(4)$, which means you need to evaluate the composition of $f(x)$ and $g(x)$ at $x = 4$. The given functions are:

$f(x) = -3x - 14$ $g(x) = x^2 - x - 5$

Step 1: Find $g(4)$

Substitute $x = 4$ into the function $g(x)$:

$g(4) = 4^2 - 4 - 5 = 16 - 4 - 5 = 7$

Step 2: Find $f(g(4)) = f(7)$

Now that we know $g(4) = 7$, substitute $7$ into $f(x)$:

$f(7) = -3(7) - 14 = -21 - 14 = -35$

Final Answer:

Thus, $(f \circ g)(4) = -35$.

It looks like the previously entered answer of $-182$ was incorrect, as the correct value should be $-35$.

Do you want more details or have any questions? Here are some additional related problems you can explore:

1. What is $(g \circ f)(4)$?
2. How do you find the domain of the composition $(f \circ g)(x)$?
3. Can $f \circ g$ be defined for all real numbers?
4. What happens if $g(x)$ is a more complex function, such as a rational function?
5. How would the process change if $f(x)$ or $g(x)$ were piecewise functions?

Tip: When dealing with composition of functions, always evaluate the inside function first and then use its result in the outer function!