If f: R → R defined by f(x) = 2x + 3 then f-1(x) =

The correct option is (x-3)/2.

Let's find the inverse of the function step-by-step.

A function $f\left(x\right)$ maps an input $x$ to an output $y$. The inverse function, denoted as $f^{-1}\left(x\right)$, reverses this process by mapping the output $y$ back to the original input $x$.

Step 1: Set the function equal to $y$.
We begin by writing the given function equation as:
$$y=2x+3$$

Step 2: Solve the equation for $x$ in terms of $y$.
To isolate $x$, first subtract 3 from both sides of the equation:
$$y-3=2x$$
Next, divide both sides of the equation by 2 to solve for $x$:
$$x=\frac{y-3}{2}$$

Step 3: Express the inverse function in terms of $x$.
Since $x=f^{-1}\left(y\right)$, we have:
$$f^{-1}\left(y\right)=\frac{y-3}{2}$$
Replacing the dummy variable $y$ with $x$ to write it in standard function notation gives:
$$f^{-1}\left(x\right)=\frac{x-3}{2}$$

This matches the correct option (x-3)/2.