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Show that f: RvecR , given by f(x)=x-[x]...

Show that `f: RvecR ,` given by `f(x)=x-[x],` is neither one-one nor onto.

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We have, `f(x)=x-[x]`

Injection test:

`f(x)=0` for all `x in {Z}`

So, `f` is a many-one function.

Surjection test:

Range `(f)=[0,1) neq {R}`.

So, `f` is an into function.

Therefore, `f` is neither one-one nor onto.

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  3. Show that f: RvecR , given by f(x)=x-[x], is neither one-one nor onto.

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  18. Let R be the set of real numbes. If f: RvecR ;f(x)=x^2 and g: RvecR ;g...

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