Answer: [tex]\bold{c)\quad f^{-1}(x)=\dfrac{ln(x)}{2}}[/tex]
Step-by-step explanation:
Inverse is when you swap the x's and y's and solve for y. Note: f(x) is y
[tex]y=e^{2x}\\\\\text{Swap the x's and y's:}\\x=e^{2y}\\\\\text{Apply ln to both sides:}\\ln\ x=ln\ e^{2y}\\\\\text{ln e cancels out}\\ln\ x=2y\\\\\text{Divide both sides by 2:}\\\dfrac{ln\ x}{2}=y[/tex]
