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)

Step-by-step 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.

$f^{-1}(x)=-1+ln(x-2)$