Inverse function is y = -1 + ln(x-2)
Step-by-step explanation:
To find the inverse of a function [tex]y=f(x)[/tex], we swap [tex]x \textrm{ and }y[/tex] and solve the equation to get the form [tex]y=f(x)[/tex]. This is the inverse function.
On swapping [tex]x \textrm{ and }y[/tex] in [tex]y=2+e^{(x+1)}[/tex], we get [tex]x=2+e^{(y+1)}[/tex].
[tex]x-2=e^{(y+1)}[/tex]
[tex]ln(x-2)=ln(e^{(y+1)} )=y+1[/tex]
∴ [tex]y=-1+ln(x-2)[/tex] is the inverse function.
[tex]f^{-1}(x)=-1+ln(x-2)[/tex]
