Activity 5.4.4.
Determine the domain of each of the following functions. In each case, write a sentence to accurately describe the domain.
(a)
\(\displaystyle f(x) = \frac{x^2-1}{x^2 + 1}\)
(b)
\(\displaystyle g(x) = \frac{x^2 - 1}{x^2 + 3x - 4}\)
(c)
\(\displaystyle h(x) = \frac{1}{x} + \frac{1}{x-1} + \frac{1}{x-2}\)
(d)
\(\displaystyle j(x) = \frac{(x+5)(x-3)(x+1)(x-4)}{(x+1)(x+3)(x-5)}\)
(e)
\(\displaystyle k(x) = \frac{2x^2 + 7}{3x^3 - 12x}\)
(f)
\(\displaystyle m(x) = \frac{5x^2 - 45}{7(x-2)(x-3)^2(x^2 + 9)(x+1)}\)
