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Let A = [–1, 1]. discuss whether the following functions defined on A are one-one, onto or bijective: f(x) = x/2

 Let A = [–1, 1]. 
 discuss whether the following functions defined on A are one-one, onto or bijective:
  f(x) = x/2
 

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
11 months ago
Dear Student

f: [-1, 1] → [-1, 1],
f (x) = x/2
Let f (x1) = f(x2)
x1/ 2 = x2
Thus, f (x) is one-one.
now x∈[-1, 1]
x/2 = f (x) = [-1/2, 1/2]
Hence, the range is a subset of co-domain ‘A’
thus, f (x) is not onto.
Thus, f (x) is not bijective

Thanks

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