Question

The graph of f is a subset of the domain of f. Is this always true or sometimes false?

Answer 1

if \(f:A\to B\) is a function, then the domain of \(f\) is the whole of A.

Answer 2

the graph of \(f:A\to B\) if a subset of \(A\times B\)

Answer 3

so. there's no way u can compare the domain of a function with its graph.

Answer 4

sorry *is a subset of ...

Answer 5

But the question asks, whether it is always true or sometimes false.

Answer 6

When is this ever true?

Answer 7

never

Answer 8

I have to choose either always true or sometimes false...

Answer 9

did you leave?

Answer 10

what subject is this for??

Answer 11

multivariable calculus

Answer 12

u could say "sometimes false"

Answer 13

The graph of f is the subset of codomain so it's false
so it's sometimes false

Answer 14

Ok then could you explain to me when it is true?

Answer 15

take example of simplest function

f(x)=x
domain= real numbers eg 1,2 -1 and so on
range = real numbers
so it's clearly subset of domain, isn't it?

Answer 16

Ah... ok then what is an example when the statement is false? Sorry for so many questions. :|

Answer 17

no problem. I'm here to help
\[f(x)=-\sqrt {x}\]
domain= positive real numbers
range=negative real numbers
clearly not a subset

Answer 18

Ok so one last related question. "The domain of f is a subset of the range of f. Always true or sometimes false?" I am having great difficulty in seeing how domain can be related to the range in term of subsets.

Answer 19

See my last post, is domain subset of range?

Answer 20

Would this also be sometimes false then? Based on the previous examples you showed me?

Answer 21

absolutely

Answer 22

Thank you very very much. You have cleared htis up for me really fast. Also much thanks to helder_edwin too. :D This is an awesome website

Answer 23

@hby0214 You're welcome