Problem 10
Question
Find the domain of each function. $$f(x)=\frac{1}{x+8}+\frac{3}{x-10}$$
Step-by-Step Solution
Verified Answer
The domain of the function \(f(x)=\frac{1}{x+8}+\frac{3}{x-10}\) is \((-\infty, -8)\cup(-8, 10)\cup(10, \infty)\).
1Step 1: Find the values for which the denominators are zero
Set the denominators of the fractions equal to zero and solve for x: \n\(x+8=0 \Rightarrow x=-8\)\n\(x-10=0 \Rightarrow x=10\)
2Step 2: Remove the values obtained from step 1 from the domain
The domain of the function is all real numbers except -8 and 10. In interval notation, this would be \n\((-\infty, -8)\cup(-8, 10)\cup(10, \infty)\)
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