Suppose that the functions $f$ and $g$ are defined for all real numbers $x$ as follows.
\[
\begin{array}{l}
f(x)=6 x \\
g(x)=4 x-2
\end{array}
\]
Write the expressions for $(f-g)(x)$ and $(f \cdot g)(x)$ and evaluate $(f+g)(3)$.

Answer

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Answer

$(f+g)(3) = f(3) + g(3) = 6 \cdot 3 + 4 \cdot 3 - 2 = 18 + 12 - 2 = \boxed{28}$

Steps

Step 1 ：First, we write the expressions for $(f-g)(x)$ and $(f \cdot g)(x)$.

Step 2 ：$(f-g)(x) = f(x) - g(x) = 6x - (4x - 2) = 6x - 4x + 2 = 2x + 2$

Step 3 ：$(f \cdot g)(x) = f(x) \cdot g(x) = 6x \cdot (4x - 2) = 24x^2 - 12x$

Step 4 ：Next, we evaluate $(f+g)(3)$.

Step 5 ：$(f+g)(3) = f(3) + g(3) = 6 \cdot 3 + 4 \cdot 3 - 2 = 18 + 12 - 2 = \boxed{28}$