# Find functions with given domain and range

#### xsw001

1) Find a continuous function f: (0,1)->R with f[(0,1)]=R
I couldn't think of any function except tangent, but its domain is NOT (0,1) though? Any suggestions?

2) Find a continous function f: (0,1)->R with f[(0,1)]=[0,1]
I couldn't think of any function that I know. Any suggestions?

3) Find a continuous function f: R->R this is strictly increasing and f(R)=(-1,1)
The graph is somewhat look like f(x)=x^(1/3), but not exactly though since the domain doesn't fall into (-1,1). Any suggestions?

Related Calculus and Beyond Homework Help News on Phys.org

#### Tom Mattson

Staff Emeritus
Gold Member
1) Find a continuous function f: (0,1)->R with f[(0,1)]=R
I couldn't think of any function except tangent, but its domain is NOT (0,1) though? Any suggestions?
Not a bad idea. Modify it to $f(x)=tan(ax+b)$ and figure out what $a$ and $b$ should be.

2) Find a continous function f: (0,1)->R with f[(0,1)]=[0,1]
I couldn't think of any function that I know. Any suggestions?
You're being asked to find a function whose range is [0,1]. Surely you can immediately come up with 2 examples.

3) Find a continuous function f: R->R this is strictly increasing and f(R)=(-1,1)
The graph is somewhat look like f(x)=x^(1/3), but not exactly though since the domain doesn't fall into (-1,1). Any suggestions?
I'm thinking arctangent here.

#### xsw001

Okay, I got the first and third one, but can you provide me some oscillated function for the 2nd one though? I know it has to do with 1/[x(x-1)], but the graph is not exactly in between [0,1] though.

#### Tom Mattson

Staff Emeritus
Gold Member
Why not use sine or cosine?

#### xsw001

Oh, yeah, thanks!

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving