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Hi all, I need answers and EXPLANATION to the following problems: (Please Help!)

(i)f: N --> N defined byf(x) =x^3 - 1

(ii)g: Z --> Z defined byg(x) = 2x+ 1

(iii)h: R --> R defined byh(x) =x(x+ 3)(x- 3)

(***note that N,Z,R stands for natural #, Integer, and Real # respectively..)

(a) Which of the functions are one-to-one?

(b) Which of the functions are bijections?

(c) For those that are bijections find the inverse function.

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Here's the other one:

The functionf: R --> R defined byf(x) = (3x- 1)/(x- 3) is not bijective however by suitably restricting the domain and codomain the function can be made to be bijective.

(a)State the domain and codomain that will make the function bijective.

What's a domain? codomain?

(b) Find the inverse of the bijective function.

(I can still remember a bit of inverse function.. i think.. well ill give it a try anyway)

f(x) = (3x- 1)/x- 3)

x= (3y- 1)/y- 3) "replace x with y"

x(y- 3) = 1(3y- 1)) "Cross multiplication"

xy- 3x[i/] = 3y- 1 "Will minus both sides with 3y"

xy- 3x- 3y= -1 "Will add both sides with 3x"

xy- 3y= -1 + 3x

y(x- 3) = -1 + 3x"Factor outy"

y= (-1 + 3x)/(x- 3) "Divide both sides with (x- 3)"

Is that correct??

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# F : N -> N defined by f(x) = x^3 - 1

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