Long Mcfarlane
05/07/2023 · Senior High School
For the function \( f(x)=4(x+3) \), find \( f^{-1}(x) \)
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Step-by-step Solution
To find the inverse of a function, we need to switch the roles of \( x \) and \( y \) and then solve for the new \( y \).
Given function: \( f(x) = 4(x+3) \)
Let's denote the inverse function as \( f^{-1}(x) \).
1. Replace \( f(x) \) with \( y \):
\( y = 4(x+3) \)
2. Swap \( x \) and \( y \):
\( x = 4(y+3) \)
3. Solve for \( y \):
\( x = 4y + 12 \)
\( 4y = x - 12 \)
\( y = \frac{x - 12}{4} \)
Therefore, the inverse function is:
\[ f^{-1}(x) = \frac{x - 12}{4} \]
Quick Answer
\[ f^{-1}(x) = \frac{x - 12}{4} \]
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