QuestionAugust 26, 2025

What is the inverse of the function? y=-6x+3 f^-1(x)=(-x+3)/(6) f^-1(x)=(x-3)/(6) f^-1(x)=6x-3 f^-1(x)=-3x+6

What is the inverse of the function? y=-6x+3 f^-1(x)=(-x+3)/(6) f^-1(x)=(x-3)/(6) f^-1(x)=6x-3 f^-1(x)=-3x+6
What is the inverse of the function?
y=-6x+3
f^-1(x)=(-x+3)/(6)
f^-1(x)=(x-3)/(6)
f^-1(x)=6x-3
f^-1(x)=-3x+6

Solution
4.2(176 votes)

Answer

f^{-1}(x) = \frac{-x + 3}{6} Explanation 1. Swap Variables Replace y with x and x with y: x = -6y + 3. 2. Solve for y Rearrange to isolate y: -6y = x - 3. Divide by -6: y = \frac{x - 3}{-6}. Simplify: y = \frac{-x + 3}{6}. 3. Identify the Inverse Function The inverse function is f^{-1}(x) = \frac{-x + 3}{6}.

Explanation

1. Swap Variables<br /> Replace $y$ with $x$ and $x$ with $y$: $x = -6y + 3$.<br />2. Solve for $y$<br /> Rearrange to isolate $y$: $-6y = x - 3$.<br /> Divide by $-6$: $y = \frac{x - 3}{-6}$.<br /> Simplify: $y = \frac{-x + 3}{6}$.<br />3. Identify the Inverse Function<br /> The inverse function is $f^{-1}(x) = \frac{-x + 3}{6}$.
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