function 的concept Question~2

2(i)

since f(x) is undefined when x^2 - 3x + 2 < 0
i.e. (x - 1)(x - 2) < 0 => 1 < x < 2
thus, the domain is x <= 1 and x >= 2, i.e. (-inf, 1], [2, inf)

2(ii)

since h(x) is undefined when sinx - 1/2 = 0
i.e. sin x = 1/2 => x = n(pi) + [(-1)^n](pi / 6) where n is an integer
thus, the domain is all real number except x = n(pi) + [(-1)^n](pi / 6)

2(iii)

since g(x) is undefined when |x^2 - 4| = 0
i.e. x^2 = 4 => x = 2 or -2
thus, the domain is all real number except x = 2 and x = -2

3(i)

g(x) = x^2 - 5 >= -5
thus, the range of g(x) is [-5, inf)

3(ii)

h(x) = -sqrt(x + 3) < 0
thus, the range of g(x) is (-inf, 0]

3(iii)

the range of h(t) = cot(t) is (-inf, inf)