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Figure 1.51 Voltage and current distribution on a nonterminated transmission
17. For each of the following pairs of functions, calculate f g and g f . g (x) = (x + 1)2 (a) f (x) = x 2 2x (b) f (x) = x 1 g (x) = x 2 + 2 2 (c) f (x) = sin(x x ) g (x) = cos(x 2 + x) g (x) = ln(x + 3) (d) f (x) = e x 2 2 (e) f (x) = sin(x x) g (x) = ln(x 2 + 2x) 2 g (x) = e 2x (f) f (x) = e x (g) f (x) = x(x 1)(x + 3) g (x) = (2x 1)(x + 2) 18. Consider each of the following as functions from R to R and say whether the function is invertible. If it is, find the inverse with an explicit formula. (a) f (x) = x 3 + 1 (b) g (x) = x 2 + x (c) h(x) = sgn x x, where sgn x is +1 if x is positive, 1 if x is negative, 0 if x is 0. (d) f (x) = x 3 8 (e) g (x) = e 3x (f) h(x) = cos x (g) f (x) = cot x (h) g (x) = sgn x x 2 , where sgn x is +1 if x is positive, 1 if x is negative, 0 if x is 0. 19. For each of the functions in Exercise 18, graph both the function and its inverse in the same set of axes. 20. Determine whether each of the following functions, on the given domain S, is invertible. If it is, then find the inverse explicitly. S = [1, 7] (a) f (x) = x 3 , (b) g (x) = ln x, S = [5, 10] (c) h(x) = cos x, S = [0, /2] (d) f (x) = sin x, S = [0, ] (e) g (x) = cot x, S = [ /2, 0] 2 S = [ 1, 1] (f) h(x) = x , (g) f (x) = x 2 + x, S = [2, 5] Keep Lines selected
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625 . 4 } catch(IOException exc) { Console.WriteLine(exc.Message); } log_out.Close(); } } Ill 237 SpeechCoding Techniques

