Summer Assignment 1: Problem 4
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(1 point) Suppose that
f(x) = \sqrt{x^2 - 4^2} and g(x) = \frac{4 - x}{}.
For each function h given below, find a formula for h(x) and the domain of h. Use interval notation for entering each domain.
(A) h(x) = (f \cdot g)(x).
h(x) = \sqrt{(\sqrt{4 - x}^2) - 4^2}
Domain = (-\infty, -12]
(B) h(x) = (g \cdot f)(x).
h(x) = \sqrt{4 - \sqrt{x^2 - 4^2}}
Domain = (-\infty, -4\sqrt{2}] \cup [4\sqrt{2}, \infty)
(C) h(x) = (f \cdot f)(x).
h(x) = \sqrt{(\sqrt{x^2 - 4^2} - 4)^2}
Domain = (-\infty, -4\sqrt{17}] \cup [4\sqrt{17}, \infty)
(D) h(x) = (g \cdot g)(x).
h(x) = \sqrt{4 - \sqrt{4 - x}}
Domain = [-12, 4]
