$$ \left. \begin{array} { l } { f ( x ) = 2 x - 9 } \ { g ( x ) = - 5 x + 6 } \ { ( f \circ g ) ( x ) = f ( g x ) ) } \end{array} ight. $$

Question

$$ \left. \begin{array} { l } { f ( x ) = 2 x - 9 } \ { g ( x ) = - 5 x + 6 } \ { ( f \circ g ) ( x ) = f ( g x ) ) } \end{array} ight. $$

UpStudy AI · Accepted Answer

To find the composition of the functions $$ f $$ and $$ g $$, denoted as $$ (f \circ g)(x) $$, we need to substitute $$ g(x) $$ into $$ f(x) $$.

1. **Identify the functions:**
   - $$ f(x) = 2x - 9 $$
   - $$ g(x) = -5x + 6 $$

2. **Substitute $$ g(x) $$ into $$ f(x) $$:**
   $$
   (f \circ g)(x) = f(g(x)) = f(-5x + 6)
   $$

3. **Calculate $$ f(-5x + 6) $$:**
   Substitute $$ -5x + 6 $$ into the function $$ f $$:
   $$
   f(-5x + 6) = 2(-5x + 6) - 9
   $$

4. **Distribute and simplify:**
   $$
   = 2(-5x) + 2(6) - 9
   $$
   $$
   = -10x + 12 - 9
   $$
   $$
   = -10x + 3
   $$

Thus, the composition of the functions is:
$$
(f \circ g)(x) = -10x + 3
$$
$$ (f \circ g)(x) = -10x + 3 $$

\( \left. \begin{array} { l } { f ( x ) = 2 x - 9 } \\ { g ( x ) = - 5 x + 6 } \\ { ( f \circ g ) ( x ) = f ( g x ) ) } \end{array} \right. \)