If F : R → R such that f(x) = 5x + 4 then which of the following is equal to f-1(x).

The correct option is "(x-4)/5".

To find the inverse function $f^{\&\#x2212;1}\left(x\right)$ of a given function $f\left(x\right)=5x+4$, we follow a systematic step-by-step process:

Step 1: Set the function equal to $y$
Let $y=f\left(x\right)$. This gives us the equation:
$y=5x+4$

Step 2: Solve the equation for $x$ in terms of $y$
First, subtract $4$ from both sides of the equation:
$y\&\#x2212;4=5x$
Next, isolate $x$ by dividing both sides by $5$:
$x=\frac{y\&\#x2212;4}{5}$

Step 3: Replace $x$ with $f^{\&\#x2212;1}\left(y\right)$
Since $x=f^{\&\#x2212;1}\left(y\right)$, we have:
$f^{\&\#x2212;1}\left(y\right)=\frac{y\&\#x2212;4}{5}$

Step 4: Swap the variable $y$ with $x$ to express the inverse function in terms of $x$
$f^{\&\#x2212;1}\left(x\right)=\frac{x\&\#x2212;4}{5}$

This matches the correct option "(x-4)/5".