Using the following equations, find $$ f(g(x)) $$ : $$ f(x)=-2 x+5 $$ $$ g(x)=3 x-9 $$ $$ f(g(x))=[?] x+\square $$

Question

UpStudy AI · Accepted Answer

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

Given:
- $$ f(x) = -2x + 5 $$
- $$ g(x) = 3x - 9 $$

**Step 1:** Substitute $$ g(x) $$ into $$ f(x) $$:
$$
f(g(x)) = f(3x - 9)
$$

**Step 2:** Apply the function $$ f $$ to $$ 3x - 9 $$:
$$
f(3x - 9) = -2(3x - 9) + 5
$$

**Step 3:** Distribute and simplify:
$$
-2(3x) + (-2)(-9) + 5 = -6x + 18 + 5 = -6x + 23
$$

So, 
$$
f(g(x)) = -6x + 23
$$

**Final Answer:**
$$
f(g(x)) = -6x + 23
$$
$$ f(g(x)) = -6x + 23 $$

Using the following equations, find \( f(g(x)) \) : \( f(x)=-2 x+5 \) \( g(x)=3 x-9 \) \( f(g(x))=[?] x+\square \)