If g(x) = 3 · x - 1 and [tex]f(x) = \sqrt{9-x^{2}}[/tex], then the domain of the division of f(x) by g(x) is equal to the following composite interval: [-3, 1/3) ∪ (1/3, 3] (Correct choice: A)
What is the domain of a function as a result of a binary operator
Binary operators are operators that involves two functions, there are four binary operators: (i) Addition, (ii) Subtraction, (iii) Multiplication, (iv) Division. First, we determine the domains of the functions f(x) and g(x):
f(x):
Domain - [-3, 3]
g(x):
Domain - (- ∞, + ∞)
If we divide f(x) by g(x), then we must take g(x) = 0 into account, since it leads to indetermination. In this case, x = 1/3. Then, the domain of the resulting function:
(f/g)(x):
Domain - [-3, 1/3) ∪ (1/3, 3]
If g(x) = 3 · x - 1 and [tex]f(x) = \sqrt{9-x^{2}}[/tex], then the domain of the division of f(x) by g(x) is equal to the following composite interval: [-3, 1/3) ∪ (1/3, 3] (Correct choice: A)
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