Let f Z Z be defined by fx 2x 3 What is the range of f Is f

Let f: Z Z be defined by f(x) = 2x 3

What is the range of f?

Is f onto?

Is f one-to-one?

Solution

so so x1=x2

a=2x-3

a=2(x-2)+1

a is odd

So range of f is set of all odd number

F is not onto

F is one to one

f(x1)=f(x2)=2x1-3=2x2-3

So x1=x2 hence f is one to one