Transformations of functions answers

Show that f is inverse of g and vice-versa, if
\(f(x)=x-6\) and \(g(x)=x+6\)

g(x)
\(\displaystyle=\frac{{{2}{x}^{{2}}-{3}{x}-{20}}}{{{x}-{4}}},{\quad\text{if}\quad}{x}\ne{4}\)
and
\(=kx-15\), if \(x=4\)
Evaluate the constant k that makes the function continuous.

\(\displaystyle{f}:{R}\to{R}\)
\(f(x)=7x-3\)
Prove that f is onto.

Given:
\(n=3\).
4 and 2i are zeros.
\(f(-1)=75\)
Find an nth-degree polynomial function with real coefficients

\(\displaystyle{f}:{R}\to{R}\)
\(f(x)=8x-2\)
\(f(a)=f(b)\)
\(\displaystyle{a},{b}\in{R}\)
Prove that f is one-to-one.

Given an indicated variable:
\(S=180n-360\)
Solve it for n

Show that \(f(x)=x-6\) and \(g(x)=x+6\) are inverses of each other.