12:15
Composition of Functions

Using the following equations, find :

Ask by Edwards Goodwin. in the United States

Jan 23,2025

Question

12:15 Composition of Functions Using the following equations, find $$ g(f(x)) $$ : $$ \begin{array}{c} f(x)=2 x \ g(x)=9 x+3 \ g(f(x))=[?] x+ \end{array} $$

UpStudy AI · Accepted Answer

To find the composition $$ g(f(x)) $$, we'll substitute the function $$ f(x) $$ into the function $$ g(x) $$.

**Given:**
$$
\begin{align*}
f(x) &= 2x \
g(x) &= 9x + 3
\end{align*}
$$

**Step-by-Step Solution:**

1. **Find $$ g(f(x)) $$:**
   $$
   g(f(x)) = g(2x)
   $$
   
2. **Substitute $$ f(x) = 2x $$ into $$ g(x) $$:**
   $$
   g(2x) = 9(2x) + 3
   $$
   
3. **Simplify the expression:**
   $$
   9(2x) = 18x \
   18x + 3 = 18x + 3
   $$
   
4. **Final Composition:**
   $$
   g(f(x)) = 18x + 3
   $$

**Answer:**
$$
g(f(x)) = 18x + 3
$$
$$ g(f(x)) = 18x + 3 $$

12:15
Composition of Functions

Using the following equations, find :

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12:15 Composition of Functions Using the following equations, find :