Little Mathis
02/11/2024 · Elementary School
What is \( (f-g)(x) ? \) \[ \begin{array}{l}f(x)=-x^{2}+4 x \\ g(x)=3 x+3\end{array} \]
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Tutor-Verified Answer
Step-by-step Solution
To find \( (f-g)(x) \), we need to subtract the function \( g(x) \) from the function \( f(x) \).
Given:
\[
f(x) = -x^2 + 4x
\]
\[
g(x) = 3x + 3
\]
We can express \( (f-g)(x) \) as follows:
\[
(f-g)(x) = f(x) - g(x)
\]
Substituting the expressions for \( f(x) \) and \( g(x) \):
\[
(f-g)(x) = (-x^2 + 4x) - (3x + 3)
\]
Now, we distribute the negative sign:
\[
(f-g)(x) = -x^2 + 4x - 3x - 3
\]
Next, we combine like terms:
\[
(f-g)(x) = -x^2 + (4x - 3x) - 3
\]
\[
(f-g)(x) = -x^2 + x - 3
\]
Thus, the result is:
\[
\boxed{-x^2 + x - 3}
\]
Quick Answer
\[
(f-g)(x) = -x^2 + x - 3
\]
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