Let's solve the given problem step by step.

We are given the functions:

• $f(x) = x^2 - 4x$
• $g(x) = 3x + 5$

We need to find $f(3) + g(-5)$.

Step 1: Calculate $f(3)$

Substitute $x = 3$ into the function $f(x)$:

$f(3) = 3^2 - 4(3)$ $f(3) = 9 - 12 = -3$

Step 2: Calculate $g(-5)$

Substitute $x = -5$ into the function $g(x)$:

$g(-5) = 3(-5) + 5$ $g(-5) = -15 + 5 = -10$

Step 3: Add $f(3)$ and $g(-5)$

Now, we add the results from steps 1 and 2:

$f(3) + g(-5) = -3 + (-10) = -13$

So, the value of $f(3) + g(-5)$ is $\boxed{-13}$.

Would you like further clarification or additional questions? Here are some related topics for exploration:

1. How do we compute the value of functions at specific points?
2. What are the properties of quadratic functions like $f(x) = x^2 - 4x$?
3. How do linear functions like $g(x) = 3x + 5$ behave differently from quadratic ones?
4. What does the graph of $f(x) = x^2 - 4x$ look like?
5. How do you evaluate the sum of two functions at specific points?

Tip: When adding or subtracting functions at specific values, remember to evaluate each function separately at the given point and then combine the results.