Using the following equations, find $$ g(f(x)) $$ : $$ f(x)=x^{6} $$ $$ g(x)=x+3 $$ $$ g(f(x))=x^{[?]}+\square $$

Question

UpStudy AI · Accepted Answer

To find $$ g(f(x)) $$, we will follow these steps:

1. **Identify the functions**:
   - $$ f(x) = x^6 $$
   - $$ g(x) = x + 3 $$

2. **Substitute $$ f(x) $$ into $$ g(x) $$**:
   - We need to find $$ g(f(x)) $$, which means we will substitute $$ f(x) $$ into $$ g(x) $$.

3. **Perform the substitution**:
   - Substitute $$ f(x) $$ into $$ g(x) $$:
   $$
   g(f(x)) = g(x^6) = x^6 + 3
   $$

4. **Express the result**:
   - We can express $$ g(f(x)) $$ in the form $$ x^{[?]} + \square $$:
   - Here, $$ g(f(x)) = x^6 + 3 $$.

Thus, we have:
- $$ g(f(x)) = x^{6} + 3 $$

So, the answer is:
- $$ g(f(x)) = x^{[6]} + \square $$ where $$ \square = 3 $$.
$$ g(f(x)) = x^{6} + 3 $$

Using the following equations, find \( g(f(x)) \) : \( f(x)=x^{6} \) \( g(x)=x+3 \) \( g(f(x))=x^{[?]}+\square \)