Math Is Fun Forum

xsw001

Member

Registered: 2010-10-23

Posts: 7

Find functions with given domain and range

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?

Last edited by xsw001 (2010-10-23 05:29:03)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Find functions with given domain and range

Hi xsw001

3) How about y = (2/pi)arctan (x) ................  arctan is inverse function of tan taking 'principle value' -pi/2 < y < +pi/2

Let me know if what you think of this.

Still working on 1) and 2)

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob