Question
Watch the video and then solve the problem given below.
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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.)
Click here to watch the video.opens in a new tab
Find the inverse of g(x)equals9xplus8.
Question content area bottom
Part 1
gSuperscript negative 1(x)equals
enter your response here (Simplify your answer.)
Answers
Answered by
GPT-4o mini
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:
\[
g^{-1}(x) = \frac{x - 8}{9}
\]
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:
\[
g^{-1}(x) = \frac{x - 8}{9}
\]
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