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Functions: Mapping

For the functions f defined below, determine which are 1:1, onto or both.

1) f: R onto R, f(x) = |x|

2) f: R onto R, f(x) = x^2 + 3

3) f: R onto R, f(x) = x^3 + 3

4) f: R onto R, f(x) = x(x^2-4)

5) f: R onto R, f(x) = |x| + x

6) f: N onto N, f(x) = x + 1

7) f: N onto NxN, f(x) = (x,x)

8) f: NxN onto N, f(x,y) = 2x + y

9) f: R^2 onto R^2, f(x,y) = (x+y , x-y)

10) f: R^2 onto R^2, f(x,y) = (x+y , x^2-y^2)

Solution Preview

1) f: R onto R, f(x) = |x|
No. because f(-x) = f(x)

2) f: R onto R, f(x) = x^2 + 3
No. because f(-x) = f(x)

3) f: R onto R, f(x) = x^3 + 3
Yes, we can never find f(a)=f(b) if a isn't equal b

4) f: R onto R, ...

Solution Summary

The mapping of functions is investigated.

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