Class XII ISC Maths Chapter Relation and Functions Exercise 1.2
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class 12 relation&function exercise1-1
Relations & Functions
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Q1 A function is defined by f(x) = 3x2+ 2x -1 / x+1 , x ∈ R , x ≠ -1 . Find the value of f (-3) + 1
Q2 Is the relation f defined f(x) = {(x2 , 0 ≤ x ≤ 3),(2x , 3 ≤ x ≤ 5)} a function ? Justify your answer.
Q3 A real function is defined by f(x) = 3x-2 x ∈ R, find the value of f(-3) + f(0) x f(7)
Q6 A function is given by the formula f(x) = 144 — 16x2, Calculate f(2). Also find the Values of x when f(x) = 0,
Q7 A function 'f' is defined by f(x) = 2x2 + 3, for all x € R. Find
(i)image of -1 under f
(ii) element (elements) of the domain which has image 35.
Q8 If f(x) = 2x2 +1 and domain of f = {-2, -1, 0, 1, 3}, find
(i) range of f
(ii) f (3) x f (-2)
(iii) x if f(x) = 9
Q9 A function 'f' is defined by f(x) = x2 + 3,x € N and x ≤ 5.
(i) Find the range of f,
(ii) Find f(2) x f(5),
(iii) Does f(-3) exist ?
(iv) Find x when f(x) = 7.
Q10 Find the domain of the following real functions -
(i) f(x) = x2 -4 / x+2
(ii) f(x) = 3x / 28 - x
(iii) f(x) = x / x2+ 3x + 2
(iv) f(x) = x3 - x + 3 / x2- 1
Q11 Find the domain of the following real functions:
(i) f(x) = √(x-2)
(ii) f(x) = √(2-3x)
(iii) f(x) = 1 / √(x-1)
(iv) f(x) = 1 / √(3-x)
Q12 Find the domain of the following real functions :
(i) f(x) = |x+2|
(ii)f(x) = -|x - 2|
(iii) f(x) = 2-|x - 1|
(iv) f(x) = |x| - x / √2x
Q13 Find the range of the following functions :
(i) f(x)= x2 + 2 , x ∈ R
(ii) f(x) = 3 - 2x , x ∈ R, x ≥ 1.
Q14 Find the domain and the range of the function f(x) = 2x2 + 1. Also find f(-2) and the numbers which are associated with the number 51 in its range. s
Q15 Find the domain and the range of the following functions :
(i) f(x) = √(x+2)
(ii) f(x) = √(3-2x)
(iii) f(x) = 1 / √(x-5)
Q16 Find the domain and the range of the following functions :
(i) f(x) = 4-x / √x-4
(ii) f(x) = x2 - 9 / √x-3
(iii) f(x) = x + 1 / 2x + 1
(iv) f(x)= 4+x / 4-x
Q17 Find the domain and the range of the following functions :
(i) f(x)= √(16-x2)
(ii) f(x)=√(x2 - 9)
(iii) f(x)= 1 / √4-x2
Q18 Find the domain and the range of the following functions :
(i) f(x) = |x - 3|
(ii) f(x) = 3-|x -2|.
Q24 Find the range of the following functions :
(i) f(x) = 2 -3 cos x
(ii) f (x) = 2 + 5 sin 3x.
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