Functions: Mapping
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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)
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Solution Summary
The mapping of functions is investigated.
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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, ...
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