f: R→R, f(x)= (2x-5)/(2x+3) is it onto function?

Question

is it's codomain= range??

Answer 1

To be onto, every value of f(x) (the codomain) must have a corresponding x.

The domain and codomain consist of all real numbers.

If y=f(x)=(2x-5)/(2x+3), then 2xy+3y=2x-5, 2xy-2x=-(5+3y), x(2y-2)=-(5+3y), x=-(5+3y)/(2y-2).

When y=1, x cannot be defined. This means that 1 in the codomain has no corresponding x value. Nothing maps to 1. Another way of looking at it is to write 1=(2x-5)/(2x+3), 2x+3=2x+5 is never true, so 1 can’t be mapped and f(x) is not an onto function.