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Determine whether the function has an inverse function. \[ g(x)=\frac{x+1}{8} \] Yes, \( g \) does have an inverse. No, \( g \) does not have an inverse. If it does, then find the inverse function. (If an answer does not exist, enter DNE.) \( g^{-1}(x)= \)

Ask by Lindsey Hill. in the United States
Mar 13,2025

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\( g^{-1}(x) = 8x - 1 \)

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Beyond the Answer

Yes, \( g \) does have an inverse. To find the inverse function, we start with the equation \( y = g(x) \): \[ y = \frac{x + 1}{8} \] Now, solve for \( x \): 1. Multiply both sides by 8: \[ 8y = x + 1 \] 2. Subtract 1 from both sides: \[ x = 8y - 1 \] Now, switch \( x \) and \( y \) to find the inverse function: \[ g^{-1}(x) = 8x - 1 \] So, the inverse function is: \[ g^{-1}(x) = 8x - 1 \]

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