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Question
Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:
f(x) = `x/2`
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Solution
Given, A = [–1, 1]
f: [–1, 1] → [–1, 1], f(x) = `x/2`
Let f(x1) = f(x2)
`x_1/2` = x2
So, f(x) is one-one.
Also x ∈ [–1, 1]
`x/2` = f(x) = `[-1/2, 1/2]`
Hence, the range is a subset of co-domain ‘A’
So, f(x) is not onto.
Therefore, f(x) is not bijective.
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