Let A be the open interval (1, 2). Find f(A). Let A be the open interval (-2, 2)

Question

Let A be the open interval (1, 2). Find f(A). Let A be the open interval (-2, 2). Find f(A). Let A be the open interval (-1, 2). Find f(A). Let A be the open interval (0, 2). Find f(A) Let A be the closed interval [1, 2]. Find f(A). Let A be the interval (-1, 2]. Find f(A). Let A be the interval [-1, 2). Find f(A). Let B be the open interval (-1, 3). Find f-1 (B). Let B be the open interval (1, 3). Find f-1 (B). Let B be the open interval (0, 3). Find f-1 (B). Let B be the closed interval [0, 3]. Find f-1 (B). Let f: R rightarrow R be defined by f(x) = cos x.

Explanation / Answer

f(x) is an increasing function of x, therefore answers : (a) (5,11) ; (b) [3,11) as f(x) is even function, minimum will be at x=0, f(0)=3, and max at x=2; (c) [3,11) (d) (3,11) (e) [1,11] (f) [0,11) as f(-1)=f(1)=5, 0 is containd in A, therefore the "closed at 0" (g) [0,11)

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