Question
Use the given functions to find the requested informatio Find \( (f \div g)(x) \). \( f(x)=-x+5 \) and \( g(x)=x+10 \)
Ask by Hampton Brewer. in the United States
Mar 16,2025
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Answer
\[
(f \div g)(x) = \frac{-x + 5}{x + 10}, \quad x \neq -10
\]
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To find \( (f \div g)(x) \), we need to compute the division of the two functions: \[ (f \div g)(x) = \frac{f(x)}{g(x)} = \frac{-x + 5}{x + 10} \] So, the resulting function is: \[ (f \div g)(x) = \frac{-x + 5}{x + 10} \] This function can be used to analyze how \( f(x) \) changes relative to \( g(x) \) as \( x \) varies. Just remember that you can't use this function where the denominator (i.e., \( g(x) \)) equals zero, which would happen at \( x = -10 \).