For the affine transformation t: R rightarrow R defined by t(x) = 3x - 2, find e
ID: 3082434 • Letter: F
Question
For the affine transformation t: R rightarrow R defined by t(x) = 3x - 2, find each of the following: t(A), where A is the closed interval [0, 1]. t(B), where B is the open interval (- 5 , -2). Find a formula for t-1. t-1(C), where C is the closed interval [-5, 1]. t-1(D), where D is the open interval (2, 6). For the affine transformation s: R rightarrow R defined by s(x) = - 2x + 1, find each of the following: s(A), where A is the closed interval [0, 1]. s(B), where B is the open interval (- 5, -2). Find a formula for s-1. s -1(C), where C is the closed interval [-5, 1]. s-1 (D), where D is the open interval (2, 6). Let f: R rightarrow R be defined by f(x) = 2x2 + 3.Explanation / Answer
So A = [0,1] s(A) = {-2x+1 | x is in [0,1]} = [-1,1] S(B) = {-2x+1 | x is in B} = (5, 11) s-1 (x) = (1-x)/2 So s(s^-1(x)) = s ((1-x)/2) = -2 ((1-x)/2) + 1 = x d ) S^-1 (C) = [0, 3] e) S^-1 (D) = [-5/2, -1/2] These are the answers message me if you have any doubts