Using the following equations, find $$ g(f(x)) $$ : $$ f(x)=2 x^{2}+4 $$ $$ g(x)=8 x+7 $$ $$ g(f(x))=[?] x^{2}+\square $$

Question

UpStudy AI · Accepted Answer

To find $$ g(f(x)) $$, we need to compose the functions $$ f $$ and $$ g $$. Here's how to do it step by step:

1. **Given Functions:**
   $$
   f(x) = 2x^{2} + 4
   $$
   $$
   g(x) = 8x + 7
   $$

2. **Compose $$ g(f(x)) $$:**
   $$
   g(f(x)) = g(2x^{2} + 4)
   $$
   
3. **Substitute $$ f(x) $$ into $$ g(x) $$:**
   $$
   g(2x^{2} + 4) = 8(2x^{2} + 4) + 7
   $$
   
4. **Expand and Simplify:**
   $$
   8(2x^{2} + 4) + 7 = 16x^{2} + 32 + 7 = 16x^{2} + 39
   $$
   
So, the composed function $$ g(f(x)) $$ is:
$$
g(f(x)) = 16x^{2} + 39
$$

**Final Answer:**
$$
g(f(x)) = 16\,x^{2} +\,39
$$
$$ g(f(x)) = 16x^{2} + 39 $$

Using the following equations, find \( g(f(x)) \) : \( f(x)=2 x^{2}+4 \) \( g(x)=8 x+7 \) \( g(f(x))=[?] x^{2}+\square \)

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