Question

What is the inverse function of \(f(x)=2 x-4\)?

Answer 1

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,

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