# What are examples of a function which is (a) onto but not one-to-one; (b) one-to-one but not onto, with a domain and range of #(-1,+1)#?

Examples

onto but not one-to-one:

one-to-one but not onto:

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(a) An example of a function that is onto but not one-to-one with a domain and range of (-1, +1) is ( f(x) = x^2 ).

(b) An example of a function that is one-to-one but not onto with a domain and range of (-1, +1) is ( g(x) = \frac{x}{2} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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