Question

Professor Gaekwad develops a machine which  can add, subtract, combine and evaluate any two  functions. It has an input machine which can accept  the functions within its domain. It has an output  unit which displays the result and a processor used  for calculations. He gives the inputs as f(x) = cos x  and g(x) = x 2 .


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Question 1

The domain of f(x) is  _______. 
(a) [0, ๐œ‹]                 (b) [–1, 1]
(c) [(-π)/2,π/2]        (d) R

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Question 2

The range of g(x) is  _______. 
(a) [0, 1]          (b) [–1, 1] 
(c) R               (d) [0, ∞)

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Question 3

( f + g )(0) =  _______. 
(a) 0              (b) 1 
(c) –1            (d) 2

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Question 4

fog (x) =  _______. 
(a) cos 2 x   (b) cos(x 2
(c) 2cos x   (d) cos 2

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Question 5

gof(x) = is  _______. 
(a) cos 2 x   (b) cos(x 2
(c) 2cos x   (d) cos 2

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  1. Chapter 1 Class 12 Relation and Functions (Term 1)
  2. Serial order wise

Transcript

Question Professor Gaekwad develops a machine which can add, subtract, combine and evaluate any two functions. It has an input machine which can accept the functions within its domain. It has an output unit which displays the result and a processor used for calculations. He gives the inputs as f(x) = cos x and g(x) = x2. Question 1 The domain of f(x) is _______. (a) [0, ๐œ‹] (b) [โ€“1, 1] (c) [(โˆ’๐œ‹)/2,๐œ‹/2] (d) R Given, f(x) = cos x Domain means all possible values of x Here, x can be any real number โˆด Domain = R So, the correct answer is (d) Question 2 The range of g(x) is _______. (a) [0, 1] (b) [โ€“1, 1] (c) R (d) [0, โˆž) Given, g(x) = x2 Range means all possible values of g(x) Since x2 โ‰ฅ 0 Hence, range is all positive values โˆด Range = [0, โˆž) So, the correct answer is (d) Question 3 (f + g)(0) = _______. (a) 0 (b) 1 (c) โ€“1 (d) 2 Given, f(x) = cos x & g(x) = x2 Now, (f + g)(0) = f(0) + g(0) = cos 0 + 02 = 1 + 0 = 1 So, the correct answer is (b) Question 4 fog (x) = _______. (a) cos2 x (b) cos(x2) (c) 2cos x (d) cos 2 Given, f(x) = cos x & g(x) = x2 Now, fog(x) = f(g(x)) = f(x2) = cos (x2) So, the correct answer is (a) Question 5 gof(x) = is _______. (a) cos2 x (b) cos(x2) (c) 2cos x (d) cos 2 Given, f(x) = cos x & g(x) = x2 Now, gof(x) = g(f(x)) = g(cos x) = (cos (x))2 = cos2 x So, the correct answer is (a)

About the Author

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.