Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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- answer these question pleasearrow_forwardLet R, S, and T be sets. Let f: R -» S, and g: S -» T be maps. Assume we know that qf is 1-1 Must f be 1-1? Either prove that it is or find a counterexample (a) Must g be 1-1? Either prove that it is or find a counterexample (b)arrow_forwardestimate the type of the function at the interval {(1,2), (2,5), (3,5), (4,7)} is it: 1-1 or onto..?arrow_forward
- 2. Let f be a function from the set {a, b, c, d] to the set {0, 4, -1,8} defined as f(a) = 4, f(c) = 0,f(b) = 8. Determine the following: a) Domain c) Range d) Image of 3 e) Pre-image of 2 i) j) k) Is f one-one? Is f on-to? Isf one-one corresponding, if so, find the inverse?arrow_forwardc) Let the set A = {-1,0, 1} and consider the following function: f3 A × A → A × A given by f(x,y) = (y7,x). Decide whether this function is injective, surjective, a bijection. f3 is an injection: Not Answered • ƒ3 is a surjection: Not Answered f3 is a bijection: Not Answered d) Let the set A = {1, 2, 3,4} and let P(A) denote the power-set of A. Consider the following function: f₁ : P(A) → P(A) given by ƒ(B) = {1, 2, 3}\B. Decide whether this function is injective, surjective, a bijection. f4 is an injection: Not Answered f4 is a surjection: Not Answered • f is a bijection: Not Answeredarrow_forwardHow to prove the following: if A ⊂ image f then f(f -1(A)) = A.arrow_forward
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