The function (f/g)(x) represents the quotient of f(x) and g(x). Therefore, to determine the domain of (f/g)(x), we need to consider the domains of both f(x) and g(x) and find where they intersect.
First, let's consider the domain of f(x) = 1/x. Since division by zero is undefined, the denominator cannot be zero. Therefore, x ≠ 0. The domain of f(x) is all real numbers except zero, or (-∞, 0) U (0, ∞).
Next, let's consider the domain of g(x) = √(x + 8). The square root function is defined for non-negative real numbers. Therefore, x + 8 ≥ 0, which means x ≥ -8. The domain of g(x) is all real numbers greater than or equal to -8, or [-8, ∞).
To find the domain of (f/g)(x), we need to find where the domains of f(x) and g(x) intersect. In this case, the domain is the intersection of the two domains.
Therefore, the domain of (f/g)(x) is the set of all real numbers except zero and all real numbers greater than or equal to -8, which can be written as (-∞, -8] U (0, ∞).
Determine the domain of (f/g)(x) when f(x)=1/x and g(x)= sqrt x+8
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