<image>Based on the block diagram shown in the image, answer the following questions.  
$$(1)$$ To make the output value $$y$$ equal to $$10$$, what should the input value $$x$$ be? 
$$(2)$$ Considering $$x$$ as the independent variable and $$y$$ as the function value, write the analytical expression of the function $$y = f(x)$$;