9. Show that (i) \( \binom{n+2}{2}-\binom{n}{2}=n+\frac{1}{2} \) Solution:

[a] Find the S.S. of the equation in \( \mathbb{R}:\left(x^{2}+4\right)\left(x^{2}-9\right)=0 \)

3.) The function \( g \) is related to one of the parent functions \( g(x)=-(x-2)^{\wedge} 3 \) a.) Identify the parent function \( f \). b.) Use function notation to write \( g \) in terms of \( f \).

Solve the following inequality: \[ \frac{r}{2}+15>45 \]

Reduciendo la siguiente expresión \( \sqrt{\frac{20^{x+1}}{4^{x+2}+2^{2 x+2}}} \)

2.) The function \( g \) is related to one of the parent functions \( g(x)=x 2-3 \) The parent function is: \( f(x)=x^{\wedge} 2 \) Use function notation to write \( g \) in terms of \( f \).