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Question
Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:
g(x) = |x|
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Solution
Given, A = [–1, 1]
Let g(x1) = g(x2)
|x1| = |x2|
x1 = ± x2
So, g(x) is not one-one
Also g(x) = |x| ≥ 0, for all real x
Hence, the range is [0, 1], which is subset of co-domain ‘A’
So, f(x) is not onto.
Therefore, f(x) is not bijective.
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