Question

"3) For the above functions,

(a) Determine if the function is injective. Justify your
answer.
(b) If it is not injective, (if possible) find the largest subset
of the domain for which the function will"
A) The entire domain.
B) A specific subset (please specify).
C) The function is always injective regardless of the subset.
D) Not enough information provided to determine the largest injective subset.

Answer 1

Without the specific function provided in the question, we can't determine if it's injective or find the largest injective subset. Injectivity means that for any two elements in the domain, if they're assigned the same value by the function, they must be the same element.

Step-by-step explanation:

The question asks about determining whether a function is injective, and if not injective, finding the largest subset of the domain where the function is injective. To check if a function is injective, we must verify if every element of the range is mapped to by at most one element of the domain. Without a specific function provided, we cannot assess injectivity definitively. However, we can explain the process generally.

For a function to be injective, it must satisfy the property that if f(a) = f(b), then a must equal b for any a and b in the domain of the function. If the function does not satisfy this condition, it is not injective over its entire domain. However, we might still find a subset of the domain for which the function is injective.

Answering part (a), we need the actual function to determine injectivity. For part (b), without a given function, we cannot specify the largest injective subset. The ideal subsets would depend on the specific character of the function in question, such as its graph or formula.