The following function is one-to-one. Find the inverse of the function and graph the function and its inverse on the same set of axes.
$f (x) = 2 x - 1$
$f^{- 1} (x) =$
(Type a simplified fraction.)

Answer

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Answer

$f^{- 1} (x) = \frac{x}{2} + \frac{1}{2}$ is the final answer.

Steps

Step 1 ：The given function is $f (x) = 2 x - 1$ .

Step 2 ：To find the inverse of a function, we swap the x and y (or f(x)) values. This means we replace every x in the original function with y and solve for y.

Step 3 ：Replacing x with y in the original function, we get $f (y) = 2 y - 1$ .

Step 4 ：Solving this equation for x, we get $x = \frac{y}{2} + \frac{1}{2}$ .

Step 5 ：So, the inverse of the function $f (x) = 2 x - 1$ is $f^{- 1} (x) = \frac{x}{2} + \frac{1}{2}$ .

Step 6 ： $f^{- 1} (x) = \frac{x}{2} + \frac{1}{2}$ is the final answer.

The following function is one-to-one. Find the inverse of the function and graph the function and its inverse on the same set of axes.f(x)=2x−1f−1(x)=(Type a simplified fraction.)

Answer

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The following function is one-to-one. Find the inverse of the function and graph the function and its inverse on the same set of axes.
$f (x) = 2 x - 1$
$f^{- 1} (x) =$
(Type a simplified fraction.)