Question 1: Find the domain of each of the following real valued functions of real variable:

Answer:

Question 2: Find the domain of each of the following real valued functions of real variable:

Answer:

assumes real values

Hence the Domain

assumes real value if

Hence the Domain

Question 3: Find the domain of each of the following real valued functions of real variable:

(

Answer:

will assume real values for all except for the value of for

Clearly will take real value for all except for

will assume real values for all except for the value of for

Clearly will take real value for all except for

assumes real value if

, we have

Thus takes all real values greater than equal to

assumes real value if

, we have

Thus takes all real values greater than equal to

is defined for all except for which

Left

is defined for all

for all

is defined for all

It can be observed that the range of is all real except positive real numbers.

will assume real values for all except when

will be real

will assume real values for all

For any value such that , the value of will lie between

will assume real values when

mean

will assume real values for all

will take real values greater that equal to .