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What is the inverse function of \(f(x)=2 x-4\)?
in Mathematics by Platinum (163,814 points) | 9 views

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An inverse function, denoted by $f^{-1}$, is a function that "undoes" the work of the original function. To find the inverse function of $f(x) = 2x - 4$, we need to switch the roles of x and y and then solve for x. So, the inverse function is defined as $f^{-1}(y) = x$

Now, we need to replace \(y\) with the original function $f(x)$ and solve for \(x\):

$f^{-1}(f(x)) = x$ $f^{-1}(2x-4) = x$

Now, we need to solve for x, $x = f^{-1}(2x-4)$

So the inverse function is,

$f^{-1}(x) = \dfrac{x+4}{2}$
by Platinum (163,814 points)

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