Problem 63
Question
Find the domain of the function. $$g(x)=\frac{1}{x}-\frac{3}{x+2}$$
Step-by-Step Solution
Verified Answer
The domain of the function \(g(x)\) is all real numbers except \(x=0\) and \(x=-2\).
1Step 1: Identify the Denominators
For this function, there are two fractions. The denominators for these fractions are 'x' and 'x+2'.
2Step 2: Solve for Undesirable Values
The function is undefined when the denominator is zero. So, identify the values of x that cause either denominator to be zero by solving the two equations \(x=0\) and \(x+2=0\). Solving these equations yields \(x=0\) for the first equation and \(x=-2\) for the second equation.
3Step 3: Exclude Undesirable Values
The domain of a function includes all the values that x can be except the undesirable values identified in Step 2. So, the domain of the function \(g(x)\) are all real values except \(x=0\) and \(x=-2\).
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