What is (f–g)(x)?f(x)=3x2+10xg(x)=x2–3xWrite your answer as a polynomial or a rational function in simplest form.
Question
What is (f–g)(x)?f(x)=3x2+10xg(x)=x2–3xWrite your answer as a polynomial or a rational function in simplest form.
Solution
To find (f-g)(x), we need to subtract the function g(x) from f(x).
f(x) = 3x^2 + 10x g(x) = x^2 - 3x
So, (f-g)(x) = f(x) - g(x) = (3x^2 + 10x) - (x^2 - 3x)
Now, distribute the negative sign to each term in the parentheses:
= 3x^2 + 10x - x^2 + 3x
Combine like terms:
= (3x^2 - x^2) + (10x + 3x)
= 2x^2 + 13x
So, (f-g)(x) = 2x^2 + 13x. This is the simplest form of the polynomial.
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