Determine algebraically if the function f(x) = 8x - 3 is onto or not.

Question

Given that f:R→R

Answer 1

One-to-One and Onto are different.

 

In this case they almost seem the same.  Basically for a function to be ONTO it must take care of all values in the range.  In this case you need to ask can all possible real numbers be in the range?  The answer is Yes, so it is ONTO.

 

Here's a good video  https://www.youtube.com/watch?v=Lk7y9L0pTgk

 

Notice that towards the end of the video she shows a cubic function which shows it is possible to be ONTO but NOT one to one.

Answer 2

Your phrase "onto or not' probably should be "one-to-one, or not."

 

For a function to be one-to-one, it must be strictly increasing, or strictly decreasing.  The former applies, because this is a straight line with positive slope.

 

Therefore it's 1-to-1, which guarantees that it has an inverse (also a function).