Let A denote the set of all real numbers. Let B denote the same set as A. Let f
be the function that, to each number in A assigns the square of the number. Is f a
function? Explain in complete sentences

Question

Let A denote the set of all real numbers. Let B denote the same set as A. Let f
be the function that, to each number in A assigns the square of the number. Is f a
function? Explain in complete sentences

zzr0ck3r · Answer

$$is \space f(x) = \pm\sqrt{x}\space a \space function?$$

amriju · Answer

can a function have two values for a point??

zzr0ck3r · Answer

this question does not give enough information. you can have either yes or no as an answer.

amriju · Answer

I meant can a function have the same value for two points??

zzr0ck3r · Answer

not by the definition of a function....

amriju · Answer

then any point x and -x will have the same value for f(x) thats a^2..so would this be a function from A to B??

zzr0ck3r · Answer

let A = B = {0}
f:A-->B,f(x) = sqrt(x). 
then the answer is yes

but if we let
A = B = R
f:A-->B,f(x) = sqrt(x)
then no

zzr0ck3r · Answer

not If A and B are {0} because sqrt(0) = 0

amriju · Answer

but A nd B are sets containing all real numbrs by ques..

zzr0ck3r · Answer

Ohh lol woops

zzr0ck3r · Answer

then no its not a function:)

amriju · Answer

:)..