# Important Questions for Class 12 Chapter 1 - Relation and Function

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**Important questions based on NCERT syllabus for Class 12 Chapter 1 - Relation and Function:**

*Question 1*: Find the domain and Range of the function x^2-4/x-2

*Solution*: Let f(x) = x^2-4/x-2

If we simplify f(x) we get x+2

Hence the domain of the function R and Range is also Range

*Question 2*: Given that 3x - 4 and g(x) = (x-2)/3. Determine (fog)(x) and (gof)(x)

*Solution*: (fog)(x) = 3g(x) - 4 = 3((x-2)/3) - 4 = x - 6

(gof)(x) = (f(x)-2)/3 = (3x - 4 - 3)/3 = 3x - 7/3

*Question 3*: For any function f(x) = x + 1, determine the range when the domain = {-6, -4, -2, 0, 2, 4 , 6}

*Solution*:

For the given values of x, we have

f(-6) = -6 + 1 = -5

f(-4) = -4 + 1 = -3

f(-2) = -2 + 1 = -1

f(0) = 0 + 1 = 1

f(2) = 2 + 1 = 3

f(4) = 4 + 1 = 5

f(6) = 6 + 1 = 7

Hence, we can write the given function as a set of ordered pairs as follows:

{(-6, -5), (-4, -3), (-2, -1), (0, 1), (2, 3), (4,5), (6,7)}

And, the range of the function = {-5, -3, -1, 1, 3, 5, 7}

*Question 4*: Let A = {2,3,4}. Find one to one function from A to A.

*Solution*: {(2,2)(2,3)(2,4)}{(3,3)(3,4)(3,2)}{4,4)(4,2)(4,3)}

{(2,2)(3,4)(4,3)}{(2,4)(3,3)(4,2)}{(2,3)(3,2)(4,4)}