Answer: [tex]\bold{d)\quad f^{-1}(x)=\dfrac{e^x}{5}}[/tex]
Step-by-step explanation:
To find the inverse, swap the x's and y's and solve for y. Note: f(x) is y
[tex]y = ln(5x)\\\\\text{Swap the x's and y's:}\\x=ln(5y)\\\\\text{Apply e to both sides:}\\e^x=e^{ln(5y)}\\\\e^{ln}\ \text{cancels out:}\\e^x=5y\\\\\text{Divide both sides by 5:}\\\dfrac{e^x}{5}=y\\\\\large \boxed{f^{-1}(x)=\dfrac{e^x}{5}}[/tex]
