Using the following equations, find $$ f(g(x)) $$ : $$ f(x)=x^{2} $$ $$ g(x)=x-1 $$ $$ \left.f(g(x))=[?] x^{2}+\square x+\square\right] $$

Question

UpStudy AI · Accepted Answer

To find $$ f(g(x)) $$ given the functions $$ f(x) = x^2 $$ and $$ g(x) = x - 1 $$, follow these steps:

1. **Compose the Functions:**
   
   $$ f(g(x)) = f(x - 1) $$

2. **Apply the Function $$ f $$ to $$ g(x) $$:**
   
   $$ f(x - 1) = (x - 1)^2 $$

3. **Expand the Square:**
   
   $$
   (x - 1)^2 = x^2 - 2x + 1
   $$

So, the composed function $$ f(g(x)) $$ is:

$$
f(g(x)) = x^2 - 2x + 1
$$

**Filled in the placeholders:**

$$
f(g(x)) = [1]x^2 + [-2]x + [1]
$$
$$ f(g(x)) = x^2 - 2x + 1 $$

Using the following equations,
find :