# Domain and Range of functions

1. Sep 2, 2010

### swatmedic05

Could someone please explain to me what the range and domain of a function is and how to find them? I just don't understand what they mean
Thank You

2. Sep 2, 2010

### Staff: Mentor

The domain of a function is the set of all valid inputs to the function. The range is the set of all possible outputs.

For example, if f(x) = 1/x2, the domain is all real numbers except 0. The range is all real numbers greater than 0.

D = {x in R | x $\neq$ 0}
R = {y in R | y > 0}

3. Sep 2, 2010

### Willian93

Domain is all the possible values that X could be
Range is all the possible values that Y could be

example: determine the domain and range of y= x^2

when u sketched the graph, you can see x could be anything, it keeps going forever there for D( -infinity, +infinity)

for y, however, you can see y never goes below x axis, the maximum value for y is just 0
therefore (0, +infinity), because y goes up forever.

4. Sep 2, 2010

### swatmedic05

But domain and range cant share a common number Can they?

5. Sep 2, 2010

### Staff: Mentor

Sure, why not?

6. Sep 3, 2010

### HallsofIvy

Staff Emeritus
They don't have to but they certainly can.

For example, the domain and range of f(x)= 2x+ 1 are both "all real numbers". Given any real number, I can certainly multiply it by 2 and then add 1- the domain is all real numbers. On the other hand, for any real number x, f(x)= 2x+ 1= y if 2x= y- 1 or x= (y- 1)/2 which is a real number. Since I can get any real number as a result of f(x) the range is all real numbers.

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