If the point \((7, 43)\) is on the graph of \(f(x)\), this means that \(f(7) = 43\).
To find the corresponding point on the graph of \(-f(-x)\), we first need to interpret the transformations applied to \(f(x)\):
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The \(-x\) means we need to find \(f(-x)\). We substitute \(-x\) into the function. If we want to find \(f(-7)\), we can use the property of the original function: since \(f(7) = 43\), we cannot directly conclude \(f(-7)\) from this information because there's no symmetry assumed about \(f\).
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The \(-f(-x)\) then negates whatever output is from \(f(-x)\). If we were to assume that \(f\) behaved regularly (e.g., it's a linear function or symmetric), we might want to use the symmetry or explore further.
However, without any additional specifics about the behavior of \(f\) beyond a single point, we can still analyze the transformations directly:
Given \(f(7) = 43\):
- Replace \(x\) with \(-7\): we need to find \(-f(-(-7)) = -f(7) = -43\).
Thus, the point corresponding to \(-f(-x)\) given the original point is: \[ (-7, -43) \]
So, the answer is: \[ \text{(−7,−43)} \]