Consider the functions f(x) = x - x2, g(x) = 2x - 1 and h(x) = f(x) / g(x). Which statement is true?

Question

a) h(x) has a point of discontinuity

b) The zero of f(x) is the vertical asymptote of h(x)

c) The non-permissible value of h(x) is the zero of g(x)

d) f(x), g(x), and h(x) have the same domain

Answer 1

h(x) = f(x)/g(x) = (x-x^2)/(2x-1) = x(1-x)/(2x-1)

which has a discontinuity, at x=1/2

a) is correct, so is c) the zero of g(x) is an impermissible value for h(x), as it makes the denominator = 0

b) and d) are incorrect

vertical asymptote is not a zero of f(x), not x=0 or x=1

domain is different for h(x) which is not all real numbers, like f(x) and g(x)