Differential Equations: JEE Main 2016 Mathematics question

If   f(x) is a differentiable function in the interval (0, $\infty$) such that f (1) = 1 and $\mathop {\lim }\limits_{t \to x}$   ${{{t^2}f\left( x \right) - {x^2}f\left( t \right)} \over {t - x}} = 1,$ for each x > 0, then $f\left( {{\raise0.5ex\hbox{$\scriptstyle 3$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}} \right)$ equal to :