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April 4th, 2018, 10:28 AM  #1 
Newbie Joined: Apr 2018 From: India Posts: 4 Thanks: 0  Domain of f(x) = 1
Domain of f(x) = 1 is R, Where is the input(x) being put? is it in f(x) = 1(x^0) ? if it is, then we must exclude x = 0 from the domain as 0^0 has no definition. In this case, domain becomes R  {0}. I'm confused. Help! 
April 4th, 2018, 10:49 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,511 Thanks: 2514 Math Focus: Mainly analysis and algebra 
$f(x)=x^0$ is a different function to $g(x)=1$. It's perfectly acceptable to have a constant function. It returns the same number (1 in this case) regardless of the input. You don't have to "put" $x$ anywhere.

April 4th, 2018, 10:56 AM  #3 
Senior Member Joined: Aug 2012 Posts: 2,099 Thanks: 604  It's put into a "black box." Conceptually, the input goes into a machine whose inner workings we have no knowledge of. All we know is that whatever we put in, the number 1 comes out. We can never have any knowledge of what's "inside the function machine." It could be gears and levers, or little elves, or some other process. Of course I'm speaking conceptually. Formally, a function is just a set of ordered pairs. So there's a pair (x, 1) for every real number x. In fact that's another way we can think about the inner working of the function machine. It's a big lookup table. A number comes in, like 47. The lookup elf goes to the lookup table, finds 47 in the left column, sees that its corresponding output value is 1, and sends 1 out the output chute. Here's a picture of a function machine. 
April 4th, 2018, 11:26 AM  #4  
Senior Member Joined: May 2016 From: USA Posts: 1,206 Thanks: 494  Quote:
It is my belief that we try to introduce the abstract concept of functions far too early. Students, especially young adolescents, might grasp the concept more easily after they study specific functions and specific families of functions. Abstraction is hard. Generalization without familiarity with specific cases is hard. Mathematics seldom grew historically by developing abstract generalizations before specific instances were known. Last edited by JeffM1; April 4th, 2018 at 11:29 AM.  
April 4th, 2018, 12:02 PM  #5 
Senior Member Joined: Feb 2010 Posts: 697 Thanks: 135 
I have a remote for my cable TV. If I punch in 10, I get NBC. If I punch in 49, I get ESPN. I can punch in either 83 or 234 to get the Inspiration network. On the other hand if I punch in 16 and get half the screen PBS and half the screen ABC, then I would say that my remote is not ... wait for it ... FUNCTIONing properly.
Last edited by mrtwhs; April 4th, 2018 at 12:11 PM. 
April 4th, 2018, 02:14 PM  #6  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,915 Thanks: 774 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
April 4th, 2018, 02:32 PM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,885 Thanks: 1088 Math Focus: Elementary mathematics and beyond 
Draw a coordinate axes. Sketch the line y = 1. What is y for any value of x?

April 7th, 2018, 04:08 PM  #8 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
A lot of the problem is due to the ambiguous way the first post if phrased. When I see "f(x)= 1" I immediately think of an equation where f(x) is defined somewhere else and "f(x)= 1" is asserting that there exist a value of x such that "f(x)= 1". When you want to define a function such that the function value is 1 no matter what x is the, at a minimum say "f(x)= 1 for all x". 

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