# NCERT Class 11-Math's: Chapter –2 Relations and Functions Part 6

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**Question 12:**

Let *f* and *g* be real functions defined by and .

(a) For what real numbers?

(b) For what real numbers ?

**Answer:**

(a)

(b)

**Question 13:**

If *f* and *g* are two real valued functions defined as , then find.

(i)

(ii)

(iii)

(iv)

**Answer:**

(i)

(ii)

(iii)

(iv)

**Question 14:**

Express the following functions as set of ordered pairs and determine their range.

**Answer:**

(i)

**Question 15:**

Find the values of *x* for which the functions

are equal

**Answer:**

## Long Answer Type

**Question 16:**

Is a function? Justify. If this is described by the relation, , then what values should be assigned to and ?

**Answer:**

Yes,

**Question 17:**

Find the domain of each of the following functions given by

(i)

(ii)

(iii)

(iv)

(v)

**Answer:**

(i)

(ii)

(iii)

(iv)

(v)

**Question 18:**

Find the range of the following functions given by

(i)

(ii)

(iii)

(iv)

(**Hint:**

**Answer:**

(i)

(ii)

(iii)

(iv)

**Question 19:**

Redefine the function

**Answer:**