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Question

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Find the inverse of ​g(x)equals9xplus8.
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Part 1
gSuperscript negative 1​(x)equals
  
enter your response here ​(Simplify your​ answer.)

Answer 1

To find the inverse of the function \( g(x) = 9x + 8 \), we need to follow these steps:

1. Replace \( g(x) \) with \( y \): \[ y = 9x + 8 \]

2. Swap \( x \) and \( y \): \[ x = 9y + 8 \]

3. Solve for \( y \):

   • Subtract 8 from both sides: \[ x - 8 = 9y \]
   • Divide both sides by 9: \[ y = \frac{x - 8}{9} \]

4. Replace \( y \) with \( g^{-1}(x) \): \[ g^{-1}(x) = \frac{x - 8}{9} \]

So the inverse function is: \[ g^{-1}(x) = \frac{x - 8}{9} \]