Step 1:

The function is .

Power rule of logarithms: .

Rewrite the function using above formula.

Domain of logarithm function is defined for or in interval notation.

Therefore  domain set of  is .

Range of the logarithm function is defined as .

Therefore  range set of  is .

Vertical asymptote of the logarithmic function is  .

Therefore Vertical asymptote of is or -axis.

Step 2:

Find the inverse function of .

Consider .

The inverse function is defined implicitly by the equation .

Solve for .

Common logarithm function: if and only if .

If , then .

Therefore the inverse function is  .

Find the domain and range of .

Domain set of is and range set is .

Here , so the domain set of  is and

Range set of is .

Step 3:

Graph:

Graph the function .

Graph the inverse function

.

Solution:

Domain set of  is .

Range set of  is .

Inverse function of   is  .

Domain set of  is .

Range set of is .