Question

determine whether the given function is a permutation of R. 24.fi : RR defined by f1(x) = x + 1 25.12: R → R defined by [2(x) = x2 26. f3 : R → R defined by f3(x) = -x]

Answer 1

The given functions can be checked for permutation by examining whether each element in the domain has a unique image in the codomain.

Step-by-step explanation:

The given functions can be checked for permutation by examining whether each element in the domain has a unique image in the codomain.

1. The function f1(x) = x + 1 is a permutation of R because for every real number x, there exists a unique result of x + 1 in the codomain.
2. The function f2(x) = x^2 is not a permutation of R because it fails the horizontal line test. For example, both -2 and 2 map to the same value, 4, in the codomain.
3. The function f3(x) = -x is a permutation of R because for every real number x, there exists a unique result of -x in the codomain.