Question

The g ^-1({0}) for the function g(x)= ⌊x⌋ is ___________

(a) {x | 0 ≤ x < 1}

(b) {x | 0 < x ≤ 1}

(c) {x | 0 < x < 1}

(d) {x | 0 ≤ x ≤ 1}

This question was posed to me in homework.

This is a very interesting question from Functions in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

Correct answer is (d) {x | 0 ≤ x ≤ 1}

The best explanation: g({0}) for the function g(x) is {x | 0 ≤ x ≤ 1}. Put g(x) = y and find the value of x in terms of y such that ⌊x⌋ = y.