# NCERT Class 11-Math's: Chapter –2 Relations and Functions Part 7

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**Question 20:**

If then show that

(i)

(ii)

**Answer:**

Given:

To show:

Explanation: given

Now replace by , we get

Hence proved

**Question 21:**

Let and be two functions defined in the domain . Find

(i)

(ii)

(iii)

(iv)

**Answer:**

(i)

(ii)

(iii)

(iv)

**Question 22:**

Find the domain and Range of the function

**Answer:**

Domain of and Range of

**Question 23:**

If

**Answer:**

Given:

To prove:

Explanation: we have

Now we will replace with , we get

From equation (i), we will substitute the value of in above equation, we get

Cancelling the like terms, we get

Hence proved