The Direct Image of a Set: Definition and Example

The Direct Image of a Set: Definition and Example

[@callme_lyds]

Thank you for always being so clear with your definitions and actually going through the steps. This helps so much, you're the best!

[@TheMathSorcerer]

Thank you for saying that, it means a lot!!

[@leeming1317]

5:12 / 5:51 Sounds like chickens doing the "I just laid an egg song" I really miss my chickens :-( Somone who never raised chickens may not even hear it, but to me I have the superwoman sense of hearing my amazing chickens

[@TigerFitoff]

damn

[@aqueeqazam]

Brilliant sir👍

[@TheMathSorcerer]

thank you so much!

[@ramanujraman_]

Sir is it possible that we have a domain bigger than co domain like one example in my mind as follows Suppose we have A={1,4,9} and B={1,2} and f:A->B as f(X) is positive sqrt of x and x belong A

[@tricky778]

you have here that f(X) is the set of all f(a), a in X and X must be in itself along with all of its own subsets and B must contain the images of each subset of X and of each element of X. I'm quite suspicious. I think the self-referential definition needs some justification.

[@STEMCoreAcademy]

So is the image the same thing as the range of the function?

[@tricky778]

I think if the function is from set X then the image of X under the function is the same thing as the range of the function, but the image of any strict subset of X might be a subset of the range of the function.

[@antongabuniia1244]

ті лучший бро

[@MB-zo2xw]

what if we were asked to find the image of the interval (-pi/6,pi] under the function f: R -> R given by f(x) = sin(x) + 1? Using your method and reasoning the image I obtain is (1/2,1] but the answer says (1/2,2]. Am I missing something? Any help would be appreciated, thanks!

[@adrianschroder4847]

If you check the y values you obtain, f(pi/2) = 2 so you will have to include 2 as well :) Just remember that maxima don't have to occur on the boundary of a given set!

[@italang7721]

No idea

[@pieterviljoen1257]

“Sends it to .. “ is hardly mathematical thinking and it introduces semantic ambiguity. Now people are going to expect -> to imply some “flow”, totally erroneous. So why explain this way ?

[@IcoN377]

Why the fuck you gotta use infinity and shit instead of like 1 and 2 to be clear man im crying over here

[@sajidmunir560]

f:R to R As f(x) =x^2-x-2 If A=]-1,1[ find f(A) working how