Question

W/c one of the ff is the invers of f(x)=2+e^x+1​

A, f(x)^-1=1+e^x B, f(x)^-1=1-ln(x-2)
C, f(x)^-1=1-e^x D,f(x)^-1=1+ln(x-2)

Answer 1

Inverse function is y = -1 + ln(x-2)

Explanation:

To find the inverse of a function
`y=f(x)`, we swap
`x \textrm{ and }y` and solve the equation to get the form
`y=f(x)`. This is the inverse function.

On swapping
`x \textrm{ and }y` in
`y=2+e^((x+1))`, we get
`x=2+e^((y+1))`.

`x-2=e^((y+1))`

`ln(x-2)=ln(e^((y+1)) )=y+1`

∴
`y=-1+ln(x-2)` is the inverse function.

`f^(-1)(x)=-1+ln(x-2)`