Answer
$ a.\quad f^{-1}(x)=x-1$. See image for graphs.
$ b.\quad$
$f^{-1}(x)=x-b$
The graph of $f^{-1}$ is parallel to the graph of $f$, with the y-intercept of $-b.$
$ c.\quad$
They will be reflections of the original line, with regard to the line $y=x$
Work Step by Step
$ a.\quad$
Find the inverse:
Set $y=f(x)$. Interchange $x$ and $y$:
$y=x+1$
$x=y+1$
... solve for y
$y=x-1$
... replace y with $f^{-1}(x)$
$f^{-1}(x)=x-1$
See image for graphs.
$ b.\quad$
Finding the inverse,
set y=f(x). Interchange and y
$y=x+b$
$x=y+b$
... solve for y
$y=x-b$
... replace y with $f^{-1}(x)$
$f^{-1}(x)=x-b$
The graph of $f^{-1}$ is parallel to the graph of $f$, with the y-intercept of $-b.$
$ c.\quad$
According to the result of (b), they will be parallel and have the opposite y-intercept.
In other words, they will be the mirror image of the original line, with regard to the line $y=x.$
(Reflect the point (a,b) over the line $y=x$ by plotting (b,a).)
