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

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

Steps

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

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

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

Step 4 ：Next, we evaluate $(f + g) (3)$ .

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