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One - One function

Let A=B=[-1...

Question

Let $A = B = [- 1, 1] .$ State whether the following functions from $A$ into $B$ are one-one.
i) $f (x) = x^{2}$
ii) $g (x) = | x |$

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Solution

Solution -
i) $f (x) = x^{2}$ is not one- one in $[- 1, 1] \to [- 1, 1]$
because $f (x) = f (- x) .$
ii) $f (x) = | x |$ is not one - one in $[- 1, 1] \to [- 1, 1]$
because $f (x) = f (- x)$

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