Please give a response to below paragraph the one marked response not the question. The Question:Discuss the...

90.2K

Verified Solution

Question

Advance Math

Please give a response to below paragraph the one markedresponse not the question.

The Question:Discuss the properties of some of the commonly usedfunctions on the set of Integers and on the set of Real Numbers.(Ex. Is the exponentiation any or none of Injective, Surjective,Bijective?, etc.)

Response: An exponential function such as exp(x) = e^x is anexample of a commonly used injective function, which is a functionthat is one-to-one, meaning the elements of the domain are notmapped to the same codomain. The example, e^x is not surjectivemeaning, that the function does not have a right inverse(exp(x)^-1= e^x), in other words, every point in the codomain needsto be mapped to the domain to be considered a surjectivefunction. At first, I was a little confused about what abijection was as the definition sounds similar to an injectivefunction, but if I understand it right, a bijection refers to aone-to-one correspondence. The difference being that a bijection isa function that is injective and surjective at the same time, andthe exponential example (exp(x)=e^x) is not a bijective functionsince it is injective but not surjective.

Answer & Explanation Solved by verified expert
4.2 Ratings (792 Votes)
First let us understand the definitions of injectivesurjective and bijectiveFor that let us consider a function Each member of A is mapped to one member of B through the givenfunctionInjective or onetoone means    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students