Originally Posted by **suedenation**

Hi, does anyone how to solve the following problems:

In each of the following cases, determine if the given function is bijective. If the function is bijective, find its inverse.

(a) The function f : R -> R defined by f(x) = 2x-3

(b) The function f : Z -> Z defined by f(x) = 2x-3

I don't really know what's the difference between (a) and (b).

I've done part (a), anything wrong?

Ans: (a)

Let yER, then if xER, then

y is the image of x under f <=> f(x)=y

<=> 2x-3=y

<=> x=(y+3)/2

so each yER is the image under f of a unique image of xER.

Therefore, f is bijective and has an inverse (y+3)/2

Thanks very much!!!! :D