Which of the following equations represents the inverse of y = e2x - 9?
Accepted Solution
A:
Answer:[tex]y=\frac{1}{2} \ln(x+9)[/tex]Step-by-step explanation:The given function is[tex]y=e^{2x}-9[/tex]Interchange x and y.[tex]x=e^{2y}-9[/tex]Solve for y.[tex]x+9=e^{2y}[/tex]Take logarithm of both sides to base e.[tex]\ln(x+9)=2y[/tex]Divide both sides by 2.[tex]y=\frac{1}{2} \ln(x+9)[/tex]