Discrete Mathematics one to one and onto function

Question

Prove that the function f : R  -> R defined as f(x) = 2x + 3 for all x ε R is both one to one and onto.

Answer 1

f(x) = 2x + 3

i.e. y=2x+3  when x∈R

So, here for every element x , where x is Real , y has a distinct value.

Suppose x=1 , then y=5 .This is one to one function.

And No other value of x can mapped y to this

This is also onto, as each element of y should be mapped here

Hence proved