Determine whether the function has an inverse function. \( f(x)=\frac{15}{x^{2}} \) Yes, \( f \) does have an inverse. No, \( f \) does not have an inverse. If it does, then find the inverse function. (If an answer does not exist, enter DNE.) \( f^{-1}(x)= \)
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To determine if the function \( f(x) = \frac{15}{x^2} \) has an inverse, we first need to check if it is a one-to-one function. Since \( f(x) \) produces the same output for both \( x \) and \( -x \) (for example, \( f(3) = f(-3) = 5 \)), it fails the horizontal line test and is therefore not a one-to-one function. Thus, the answer is: No, \( f \) does not have an inverse. As for the inverse function: \( f^{-1}(x) = DNE \) (does not exist).
