For the following function in the image, can you find a restriction of the domain and codomain -

without changing the mapping rule - to make the function both injective and surjective?

(Restricting the domain and codomain means replacing it with a subset). The restricted domain

and codomains should be the largest you can think of.

To give an example, the function f: [-3..3]-> [-9..9] given by f(x) = x^2 is neither injective nor

surjective, but we can restrict the domain and codomain to f:[0..3] -> {0, 1, 4, 9} with the same

mapping rule, that is f = x^2, which is both injective and surjective. The codomain is as large as

possible because adding every other number in [-9..9] that is not a square would break

subjectivity and the domain is as large as possible because adding any negative number breaks

injectivity./nh : 2[1..n] → → [0..2n] given by h(S) = |S| where n ≥ 2.