Question

Write the inverse of the logarithmic function used to represent the situation in model 1, f(x)=3+2In x . Express the answer in radical form.

Answer 1

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

`f^(-1)(x)= e((x-3))/(2)`

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."

Answer 2

`f^(-1)(x) =e^{((x-3))/(2)}`

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

∴
`e^(x-3)=e^{lny^(2) } =y^(2)`

∴
`y=e^{((x-3))/(2)}`

- Change y to
`f^(-1)(x)`

∴
`f^(-1)(x) =e^{((x-3))/(2)}`