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Is f(x)=x/sqrt(1+x) surjective? How can we prove it #maths #olympiad #education #mit #calculus #chemistry #python #physics #howtosolveolympiadmathproblem
The aim of this video is to prove that a subjective function has some properties. First. What's a subjective function? How can we Define a subjective function? How do we know that a function is search active? In this video? We're going to give a An example Of a subjective function, and we're going to prove that it is subjective. We're going to use many algebraic techniques to prove. The following result, The aim is to prove that f is subjective by using algebra and the definition of the subjectivity of the function. We're going to use algebra to prove that the set of images. That means the order range is covered by. I the set of the domain of definition of this function, So we can prove in this case that for every element in the domain We can find, or we can prove that every element in the range. It's covered by some element in the, To the main of definition. Or we can prove that the image of the domain of definition is the whole range. So in this case, we can see that our function is search ejective. Sometimes it's not easy to prove that a function is subjective. We will use some techniques. And in this video this is one of the techniques that we can use to prove that f is subjective To prove this case. We use the fact that if we can show that the set of the old range is covered by all the element of the domain. Our function is subjective. Okay? So this is a nice example to try to train and work, some ideas using algebra and techniques from calculus one, And some pre-calculus, and maybe some algebra two techniques.