Can this be an onto function? A function

Alisa Duarte

Alisa Duarte

Answered question


Can this be an onto function?
A function f:RR, where R is set of real numbers, is defined by
Find the interval of values of α for which f is onto. Justify your answer.

Answer & Explanation

Donovan Acevedo

Donovan Acevedo

Beginner2022-03-20Added 5 answers

The question is poorly worded. They do not want the domain to be the set of real numbers, they want it to be {xR:α+6x8x20}.
In calculus and analysis it's common for functions not to be defined everywhere and many times the phrase "real valued function" means the domain is an appropriate subset of the real numbers. The proper term for this is a "partial function" but since these are so common in this area of mathematics, it's common to just call these "functions."
Whether it's still appropriate to write "f:RR" I would argue no. I've always seen f:DRR where D is an unspecified set but is assumed to be the largest subset of R for which the definition of f makes sense. It would seem that whoever wrote this textbook have a different opinion than me.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?