The Kinetic energy of an object in Joules is ,

where   represents speed of the object in meter per second.

represents  mass of object in kilograms.

(a).

The function is .

Function has an inverse if and only if no horizontal line intersects its graph of the function in at most one point.

The domain of is , since speed of the object is positive.

To find the inverse of the function, consider and solve in terms of .

Now interchange and .

Replace .

.

The inverse of is .

The inverse function represents speed of the object in , where

represents energy of the object in joules.

represents mass of object in kilograms.

(b).

Show that and are inverse functions in the domain .

if and are inverse functions, then .

.

, hence and are inverse functions.

Mass of the object is .

The function is .

The inverse function is

Graph :

Graph for the functions and .

.

(a). \ \

The inverse function respresents speed of the object in , where

represents energy of the object in joules.

represents mass of object in kilograms.

(b) and are inverse functions.

(c)

Graph for the functions and .