What is (f–g)(x)?f(x)=3x2g(x)=x2+2x+1Write your answer as a polynomial or a rational function in simplest form.
Question
What is (f–g)(x)?f(x)=3x2g(x)=x2+2x+1Write your answer as a polynomial or a rational function in simplest form.
Solution
To find (f-g)(x), we subtract the function g(x) from f(x).
f(x) = 3x^2 g(x) = x^2 + 2x + 1
So, (f-g)(x) = f(x) - g(x) = 3x^2 - (x^2 + 2x + 1)
Simplify the expression by distributing the negative sign in the parentheses:
= 3x^2 - x^2 - 2x - 1
Combine like terms:
= 2x^2 - 2x - 1
So, (f-g)(x) = 2x^2 - 2x - 1. This is the simplest form of the polynomial.
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