Answer
$(a)$ One-to-one function is a function whose each element in its range corresponds to the only one element in its domain.
$(b)$ Graphically, we can use the Horizontal Line Test to determine whether a function is one-to-one or not.
$(c)$ The range and the domain will switch each other. $f^{-1}$ will have domain $B$ and range $A$.
$(d)$ To find inverse of a function, we have to follow the next steps:
$1.$ Write the function in terms of $y$ and $x$ ($f(x)=y$)
$2.$ Switch $y$ by $x$ and vice versa
$3.$ simplify the equation for $y$
$f^{-1}=\frac{x}{2}$
$(e)$ If we are given the graph of $f$ we simply reflect it about $y=x$ line and we will get $f^{-1}$
Work Step by Step
$(a)$ One-to-one function is a function whose each element in its range corresponds to the only one element in its domain.
$(b)$ Graphically, we can use the Horizontal Line Test to determine whether a function is one-to-one or not.
The Horizontal Line Test means to visually imagine infinite amount of horizontal lines. There has to be no horizontal line that crosses the graph of a function more than one time.
$(c)$ The range and the domain will switch each other. $f^{-1}$ will have domain $B$ and range $A$.
$(d)$ To find inverse of a function, we have to follow the next steps:
$1.$ Write the function in terms of $y$ and $x$ ($f(x)=y$)
$2.$ Switch $y$ by $x$ and vice versa
$3.$ simplify the equation for $y$
$f(x)=2x$
$y=2x$
$x=2y$ //Switch
$y=\frac{x}{2}$
$f^{-1}=\frac{x}{2}$
$(e)$ Inverse of a function is reflection of the function about $y=x$ line. So, if we are given the graph of $f$ we simply reflect it about $y=x$ line and we will get $f^{-1}$