Final answer:
When combining functions f(x), g(x), and h(x) as requested, the result simplifies to 3x² + 2.
Step-by-step explanation:
To find f(x) + g(x) - h(x), we simply perform the operations indicated, combining the like terms from each function. Let's first write down each function and then combine them accordingly:
f(x) = 3x + 5
g(x) = 4x² - 2
h(x) = x² - 3x + 1
Now, adding f(x) and g(x), and then subtracting h(x), we get:
f(x) + g(x) - h(x) = (3x + 5) + (4x² - 2) - (x² - 3x + 1).
We combine like terms:
- For the x² terms: 4x² - x² = 3x²
- For the x terms: 3x + (-3x) = 0x
- For the constant terms: 5 - 2 - 1 = 2
So, f(x) + g(x) - h(x) simplifies to:
3x² + 0x + 2
Or, more simply:
3x² + 2