Answer
(a) The inverse function is defined as follows:
$$y=f(x)\Rightarrow x=f^{-1}(y).$$
Its domain is $B$ and its range is $A$.
(b) If you have the formula for $f(x)$, then you solve the equation
$$y=f(x)$$
for $x$:
$$x=f^{-1}(y)$$
(c) You symmetrically reflect the graph with respect to the line $y=x$.
Work Step by Step
(a) The inverse function is defined as follows: If the value of function $f$ at the point $x$ is $y$ then the value of the function $f^{-1}$ at the point $y$ is $x$ i.e. it satisfies:
$$y=f(x)\Rightarrow x=f^{-1}(y).$$
Its domain is the range of the function $f$ which is $B$ and its range is the domain of the function $f$ which is $A$.
(b) If you have the formula for $f(x)$ then you solve the equation
$$y=f(x)$$
for $x$ and the expression you get for it:
$$x=f^{-1}(y)$$
is the inverse function.
(c) You symmetrically reflect the graph with respect to the line $y=x$ i.e. the straight line that passes through the origin at $45^\circ$ with respect to $x$ axis (and $y$ axis).
