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And found that f is neither injective nor subjective that's important on figuring out the image How do you find the image of the interval $. If it were subjective the every real would be mapped to and the image would be the set of all real numbers

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But some numbers are not mapped to and the are not in the image I am little confused with the idea of images of a function how do you find the image of a particular interval with respect to a function The image is the set of all the numbers that are mapped to.

Are there some good overviews of basic facts about images and inverse images of sets under functions?

Despite the apparent duality between these two concepts, it is well known that inverse images are in general much better behaved than forward images. That is, $$f:p (a)\to p (b)$$ is a function that takes in a subset of the domain, say $t$, and returns the set $r$ containing the images of all the elements of $t$. Proof attempt i am guessing here $a$ and $b$ are sets in the range of $f$ You'll need to complete a few actions and gain 15 reputation points before being able to upvote

Upvoting indicates when questions and answers are useful What's reputation and how do i get it Instead, you can save this post to reference later. 33 take any open cover of f (k), as f is continuous, the inverse images of those open sets form an open cover of k

Since k is compact there is a finite subcover

By construction, the images of the finite subcover give a finite subcover of f (k), therefore f (k) is compact. Image of intersection of sects not equal to intersection of images of sets [duplicate] ask question asked 12 years, 1 month ago modified 7 years, 9 months ago I'm trying to understand intuitively why the image ( under some function ) of the intersection of subsets of the domain of that function is only contained ( and not equal ) to the intersection of.