Let be a function defined as . Then is:Question 2Answera.Injective in b.Surjective in c.Bijective in d.Neither injective nor surjective in
Question
Let be a function defined as . Then is:Question 2Answera.Injective in b.Surjective in c.Bijective in d.Neither injective nor surjective in
Solution
To determine whether the function is injective, we need to check if different inputs yield different outputs.
Let's assume two inputs, and , such that and .
Now, let's evaluate the function for these inputs:
Since the outputs are different, we can conclude that the function is injective.
To determine whether the function is surjective, we need to check if every element in the codomain has a corresponding element in the domain.
Let's consider an arbitrary element in the codomain.
Now, let's solve the equation for :
Since we were able to find an input that maps to the arbitrary element , we can conclude that the function is surjective.
Therefore, the function is both injective and surjective, which means it is bijective.
Similar Questions
For each of the following, state whether it is possible to have a function meeting the criteria given, explain why orwhy not, and if it is possible, give two examples.(a) A function f : N≥0 → N≥0 which is not surjective.(b) A function f : N≥0 → Z which is injective.(c) A function f : Q → Q which is bijective.
Let A=7,8,9 and B=7,8,9 and f is onto from A to B, then which of the following is correct?*f is bijectivef is surjectivef may or may not be bijectivef is into function
or each of the following functions, state whether it is injective, surjective, and/or bijective, and why.(a) The function f (n) = 2n, mapping from integers to integers.(b) The function q(ϕ), with codomain N≥0, which maps any formula of predicate logic to the number of quantifiersin that formula.
Determine whether the following functions are bijective.(a) f : R → R, with y = f (x) = 3x + 52(b) f : R → R, with y = f (x) = (2x − 7)2(c) f : R → R, with y = f (x) = √3x − 1
If f A —> B and g : B —> C are injectivefunction, then gof: A —> C is an injectivefunction. Prove or disprove.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.