Find value of iffn is 1-1 and onto.F=ax+3

Answer 1

A function that is one-to-one and onto means that it is bijective. A bijective function must map all of its possible inputs to all of its possible outputs.

Here, a can actually be any real number as long as it's not 0. In general, linear functions are bijections.

Informal Proof:

y = ax + 3;

We see that x itself can span all of the real numbers (trivial).

x = (y - 3)/a ; this linear combination also spans all real numbers so long as a is not 0.

QED