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Give an example of a non-invertible function f:ℝ→ℝf:R→Rff fails one of the conditions for being a...

Give an example of a non-invertible function f:ℝ→ℝf:R→Rff fails one of the conditions for being a bijection, then it will not be invertible. Can you think of a function f:ℝ→ℝf:R→RℝR
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Answer #1

A function f : A --> B is invertible if and only if it is bijective.

That is, f is one-to-one and onto. If f fails to be any of one-to-one or onto, then f is not invertible.

Now Consider a function f : --> defined by f(x) = x2.

If will be one-to-one if for x y, f(x) f(y).

Now consider x = 1 and y = - 1. Here x y.

Then, f( 1) = 1 = f(-1).

Hence, f fails to be one-to-one.

Therefore, f is not invertible.

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