Let f: R – {3/5} → R be defined by f(x) = 3x+2/5x−3 then

The correct option is f⁻¹(x) = f(x).

To understand why this is correct, let us find the inverse of the function f(x) step-by-step.
The given function is defined as:
$$f\left(x\right)=\frac{3x+2}{5x-3}$$

Let $y=f\left(x\right)$. To find the inverse function $f^{-1}\left(x\right)$, we need to express x in terms of y:
$$y=\frac{3x+2}{5x-3}$$

Multiply both sides by $(5x-3)$ to clear the denominator:
$$y(5x-3)=3x+2$$

Expand the left side of the equation:
$$5xy-3y=3x+2$$

Rearrange the terms to group all terms containing x on one side:
$$5xy-3x=3y+2$$

Factor out x from the left-hand side:
$$x(5y-3)=3y+2$$

Divide both sides by $(5y-3)$ to solve for x:
$$x=\frac{3y+2}{5y-3}$$

Since $y=f\left(x\right)$ implies $x=f^{-1}\left(y\right)$, we have:
$$f^{-1}\left(y\right)=\frac{3y+2}{5y-3}$$

Replacing the dummy variable y with x, we get the inverse function:
$$f^{-1}\left(x\right)=\frac{3x+2}{5x-3}$$

Comparing this expression with the original function, we observe that:
$$f^{-1}\left(x\right)=f\left(x\right)$$

Therefore, the inverse of the function is identical to the function itself.