To find the inverse function of the given function \( f(x) = -3x - 18 \), we'll follow these steps:
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Replace \( f(x) \) with \( y \): \[ y = -3x - 18 \]
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Swap \( x \) and \( y \): \[ x = -3y - 18 \]
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Solve for \( y \):
- First, add 18 to both sides: \[ x + 18 = -3y \]
- Next, divide both sides by -3: \[ y = -\frac{x + 18}{3} \]
- This simplifies to: \[ y = -\frac{1}{3}x - 6 \]
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Replace \( y \) with \( f^{-1}(x) \): \[ f^{-1}(x) = -\frac{1}{3}x - 6 \]
Thus, the inverse function in slope-intercept form is: \[ f^{-1}(x) = -\frac{1}{3}x - 6 \]