Final answer:
To find the domain of f ⋅ g, we take the intersection of the domains of f(x) and g(x), which is (-∞, 5/8) ∪ (5/8, ∞).The domain of f ⋅ g is (-∞, 5/8) ∪ (5/8, ∞).
Step-by-step explanation:
To find the domain of the function f ⋅ g, we need to consider the domains of both f(x) and g(x) and find their intersection.
The domain of f(x) is all real numbers except the value that makes the denominator zero. So, the domain of f(x) is (-∞, 5/8) ∪ (5/8, ∞).
The domain of g(x) is also all real numbers except the value that makes the denominator zero.
Therefore, the domain of g(x) is (-∞, 5/8) ∪ (5/8, ∞). To find the domain of f ⋅ g, we take the intersection of the domains of f(x) and g(x), which is (-∞, 5/8) ∪ (5/8, ∞).
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