Warm-up for $$ 3 / 12 $$ $$ f(x)=x^{2}+3 x-5 $$ and $$ g(x)=5 x+2 $$ 1. Find $$ f(x)+g(x) $$ 2. Find $$ g(x)^{*} g(x) $$ 3. Find $$ f(g(-2) $$

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$$
\textbf{1. Encontrar } f(x) + g(x)
$$

Dada:
$$
f(x) = x^2 + 3x - 5 \quad \text{y} \quad g(x) = 5x + 2
$$

Sumamos ambas funciones:
$$
f(x) + g(x) = (x^2 + 3x - 5) + (5x + 2)
$$
$$
= x^2 + (3x + 5x) + (-5 + 2)
$$
$$
= x^2 + 8x - 3
$$

---

$$
\textbf{2. Encontrar } g(x) \times g(x)
$$

Multiplicamos $$ g(x) $$ por sí misma:
$$
g(x) \times g(x) = \left(5x + 2\right)^2
$$

Expandiendo el cuadrado del binomio:
$$
\left(5x + 2\right)^2 = (5x)^2 + 2 \cdot 5x \cdot 2 + 2^2
$$
$$
= 25x^2 + 20x + 4
$$

---

$$
\textbf{3. Encontrar } f(g(-2))
$$

Primero evaluamos $$ g(-2) $$:
$$
g(-2) = 5(-2) + 2 = -10 + 2 = -8
$$

Luego, sustituimos $$ x = -8 $$ en $$ f(x) $$:
$$
f(-8) = (-8)^2 + 3(-8) - 5
$$
$$
= 64 - 24 - 5
$$
$$
= 35
$$

---

$$
\boxed{
\begin{aligned}
&1.\; f(x) + g(x) = x^2 + 8x - 3 \
&2.\; g(x) \times g(x) = 25x^2 + 20x + 4 \
&3.\; f(g(-2)) = 35
\end{aligned}
}
$$
1. $$ f(x) + g(x) = x^2 + 8x - 3 $$ 2. $$ g(x) \times g(x) = 25x^2 + 20x + 4 $$ 3. $$ f(g(-2)) = 35 $$

Warm-up for \( 3 / 12 \) \( f(x)=x^{2}+3 x-5 \) and \( g(x)=5 x+2 \) 1. Find \( f(x)+g(x) \) 2. Find \( g(x)^{*} g(x) \) 3. Find \( f(g(-2) \)

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