To find $(f - g)(x)$, we need to subtract $g(x)$ from $f(x)$. Here’s the step-by-step solution:

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

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

Now distribute the negative sign across $g(x)$: $= 4x^2 + 2x - 5 - x^2 + 3x - 4$

Combine like terms: $= (4x^2 - x^2) + (2x + 3x) + (-5 - 4)$ $= 3x^2 + 5x - 9$

So, $(f - g)(x) = 3x^2 + 5x - 9$

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Would you like more details or have any questions?

Here are five related questions you might find useful:

1. What is $(f + g)(x)$ for the same functions?
2. How do we find $(f \cdot g)(x)$ using $f(x)$ and $g(x)$?
3. How does this process change if you need $(f/g)(x)$?
4. What happens to $(f - g)(x)$ if we change the constants in $f(x)$ and $g(x)$?
5. How would the graph of $(f - g)(x)$ compare to the graphs of $f(x)$ and $g(x)$?

Tip: Always remember to distribute negative signs carefully when subtracting polynomials.