If the function is not onto, find its range. In every case, assume that the codo

Question

If the function is not onto, find its range. In every case, assume that the codomain is the set R. Also assume that the original domain is the largest set of real numbers for the function is well-defined. (It might be helpful to look at the graphs of the functions.) f(x) = |x|, and f/A, where A = [0,infinity ). t(x) = tan(x), and t/A, where A = (- pi /2, pi /2). v(x) = ln ex, and v/A, where A = ( - infinity,0]. For each real function whose rule is given below, find a set A of real numbers such that f/A is one-to-one. f(z) = x2 -2x + 4 f(x) = |3x - 5| f(x) = cos x f(x) = tan x .

Explanation / Answer

a) [1, infinity) b) [5/3 , infinity) c) [0, 2 pi) d) (-pi/2 , pi/2)

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