NCERT class 11 maths chapter 2 Relations and Functions
Question 1:The relation f is defined by 2 0 3 ( ) = 3 3 10 x , x f x x, x ì ≤ ≤ ïí îï ≤ ≤ The relation g is defined by 2 , 0 2 ( ) 3 , 2 10 x x g x x x ìï ≤ ≤ =í îï ≤ ≤ Show that f is a function and g is not a function.
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Question 2:If f (x) = x 2 , find (1 1) (1) (1 1 1) f . – f . – .
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Question 3:Find the domain of the function f (x) 2 2 2 1 8 12 x x x – x + + = + .
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Question 4:Find the domain and the range of the real function f defined by f (x) = (x −1) .
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Question 5:Find the domain and the range of the real function f defined by f (x) = x –1 .
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Question 6:Let 2 2 , : 1 x f x x x ìïæ ö ïü = íç ÷ Î ý îïè + ø ïþ R be a function from R into R. Determine the range of f.
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Question 7:Let f, g : R→R be defined, respectively by f(x) = x + 1, g(x) = 2x – 3. Find f + g, f – g and f g .
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Question 8:Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined by f(x) = ax + b, for some integers a, b. Determine a, b.
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Question 9:Let R be a relation from N to N defined by R = {(a, b) : a, b ÎN and a = b 2 }. Are the following true? (i) (a,a) Î R, for all a Î N (ii) (a,b) Î R, implies (b,a) Î R (iii) (a,b) Î R, (b,c) Î R implies (a,c) Î R. Justify your answer in each case.
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Question 10:Let A ={1,2,3,4}, B = {1,5,9,11,15,16} and f = {(1,5), (2,9), (3,1), (4,5), (2,11)} Are the following true? (i) f is a relation from A to B (ii) f is a function from A to B. Justify your answer in each case.
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Question 11:Let f be the subset of Z × Z defined by f = {(ab, a + b) : a, b Î Z}. Is f a function from Z to Z? Justify your answer.
Question 12:Let A = {9,10,11,12,13} and let f : A→N be defined by f (n) = the highest prime factor of n. Find the range of f.
