The problem asks to find $(f - g)(x)$, where:

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

Solution:

$(f - g)(x)$ is defined as:

$(f - g)(x) = f(x) - g(x)$

Substituting the given functions:

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

Simplify:

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

Combine like terms:

$(f - g)(x) = x^2 - 7x + 5$

Final Answer:

$(f - g)(x) = x^2 - 7x + 5$

Would you like a deeper explanation or more examples?

5 Related Questions:

1. What is the result of $(f + g)(x)$ for the same functions?
2. How do you compute $(fg)(x)$, the product of two functions?
3. What is the domain of the resulting function $(f - g)(x)$?
4. How do you find the derivative of $(f - g)(x)$?
5. How would the result change if $g(x)$ were a quadratic function instead of linear?

Tip:

When subtracting functions, always distribute the negative sign carefully to avoid errors!