If $$ f(x)=6 x $$ and $$ g(x)=2 x-7 $$, find $$ (f g)(x) $$ $$ (\mathrm{fg})(\mathrm{x})=\square $$

Question

UpStudy AI · Accepted Answer

1. Write down the given functions:
   $$
   f(x) = 6x \quad \text{and} \quad g(x) = 2x - 7
   $$

2. The product function $$(fg)(x)$$ is defined as:
   $$
   (fg)(x) = f(x) \cdot g(x)
   $$

3. Substitute the expressions for $$ f(x) $$ and $$ g(x) $$:
   $$
   (fg)(x) = 6x \cdot (2x - 7)
   $$

4. Distribute $$ 6x $$ across the terms inside the parentheses:
   $$
   (fg)(x) = 6x \cdot 2x - 6x \cdot 7
   $$

5. Multiply the terms:
   $$
   (fg)(x) = 12x^2 - 42x
   $$

Thus, 
$$
(\mathrm{fg})(x) = 12x^2 - 42x
$$
$$(fg)(x) = 12x^2 - 42x$$

If \( f(x)=6 x \) and \( g(x)=2 x-7 \), find \( (f g)(x) \) \( (\mathrm{fg})(\mathrm{x})=\square \)