To find the inverse of the function \( g(x) = -3x \), follow these steps:
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Replace \( g(x) \) with \( y \): \[ y = -3x \]
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Swap \( x \) and \( y \): \[ x = -3y \]
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Solve for \( y \): \[ y = \frac{x}{-3} \] or \[ y = -\frac{1}{3}x \]
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Replace \( y \) with \( g^{-1}(x) \): \[ g^{-1}(x) = -\frac{1}{3}x \]
Thus, the inverse function is: \[ g^{-1}(x) = -\frac{1}{3}x \]