Respuesta :

Ashraf82

Answer:

[tex]f^{-1}(x) =e^{\frac{(x-3)}{2}}[/tex]

Step-by-step explanation:

∵ f(x) = 3 + 2lnx

∵ f(x) = y

∴ y = 3 + 2ln(x)

- Switch x and y

∴ x = 3 + 2ln(y)

- Subtract 3 from both sides

∴ x - 3 = 2ln(y)

∴ x - 3 = ln(y²)

- Insert e to both sides

∴ [tex]e^{x-3}=e^{lny^{2} } =y^{2}[/tex]

∴ [tex]y=e^{\frac{(x-3)}{2}}[/tex]

- Change y to [tex]f^{-1}(x)[/tex]

∴  [tex]f^{-1}(x) =e^{\frac{(x-3)}{2}}[/tex]

reinaester523

Answer:

Also agree with answer of Part A; Question 1; Model 1

[tex]f^{-1}(x)= e\frac{(x-3)}{2}[/tex]

Explanation:

This answer only answers Model 1:

"Scientists developed a process of producing fresh water from salt water. The amount of fresh water produced from salt water in x hours can be found using a logarithmic function (base e) of f (x)= 3 + 2 In x . In the function, the number 3 represents the amount of fresh water produced after 1 hour has passed and the number 2 represents the rate of production of fresh water."

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