The function is .

(a)

Find an equation for the inverse of function .

Consider and solve for in terms of .

Take out the common term .

, .

Interchange and .

Replace by .

, .

(b)

Graph :

The functions is and inverse of the function is .

Observe the graph,

The two functions are symmetrical about the line .

and are inverse functions.

(c)

Find the relation between the graphs of the function and its inverse.

Find .

.

Find .

.

The composite function and .

The inverse of function is .

Therefore function and  are symmetric with respect to .

(d)

The functions is and inverse of the function is .

Domain is the set of values of which makes the function mathematically correct.

Domain of   is set of all real numbers except .

The domain of is set of all real numbers except .

Range is the output values of the function.

Range of the is set of all real numbers except .

Range of is set of all real numbers except .

(a)The inverse function of is .

(b)

Graph :

The functions is and inverse of the function is .

Observe the graph,

The two functions are symmetrical about the line .

and are inverse functions.

(c) The function and  are symmetric with respect to .

(d)

Domain of   is set of all real numbers except .

The domain of is set of all real numbers except .

Range of the is set of all real numbers except .

Range of is set of all real numbers except .