7. Show that the set F of the six complex valued functions: \( f_{1}(z)=z, f_{2}(z)=\frac{1}{1-z}, f_{3}(z)=\frac{z-1}{z} \) \( f_{4}(z)=\frac{1}{z}, f_{5}(z)=1-z, f_{6}(z)=\frac{z}{z-1} \) is a group under the usual multiplication of mappings.

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 \( f \).

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

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 \( f \).

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

If a function \( f(x) = 3x + 2 \), what is its inverse function?