Asked by d
For the function f(x)=4x+2, find the f^-1(x)
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Answered by
GPT-4o mini
To find the inverse function \( f^{-1}(x) \) of the given function \( f(x) = 4x + 2 \), we will follow these steps:
1. Replace \( f(x) \) with \( y \):
\[
y = 4x + 2
\]
2. Swap \( x \) and \( y \):
\[
x = 4y + 2
\]
3. Solve for \( y \):
\[
x - 2 = 4y
\]
\[
y = \frac{x - 2}{4}
\]
4. Replace \( y \) with \( f^{-1}(x) \):
\[
f^{-1}(x) = \frac{x - 2}{4}
\]
Thus, the inverse function is:
\[
f^{-1}(x) = \frac{x - 2}{4}
\]
1. Replace \( f(x) \) with \( y \):
\[
y = 4x + 2
\]
2. Swap \( x \) and \( y \):
\[
x = 4y + 2
\]
3. Solve for \( y \):
\[
x - 2 = 4y
\]
\[
y = \frac{x - 2}{4}
\]
4. Replace \( y \) with \( f^{-1}(x) \):
\[
f^{-1}(x) = \frac{x - 2}{4}
\]
Thus, the inverse function is:
\[
f^{-1}(x) = \frac{x - 2}{4}
\]
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