Question

Determine g-1(x) of the function g(x) = 1 /(2x + 6)
where x≠ -3. please help!!!!

Answer 1

put
\[y=\frac{1}{2x+6}\]then switch \(x\) and \(y\) because that is what the inverse function does, and get
\[x=\frac{1}{2y+6}\] then solve for \(y\)

Answer 2

\[x=\frac{1}{2y+6}\]
\[x(2y+6)=1\]
\[2xy+x=1\]
\[2xy=x+1\]
\[y=\frac{x+1}{2x}\]