Calculating the bandwidth of multi variable function

Dear all, I have the following gain spectrum

 y=(1./((f.^2)+1))-(p./((f+w).^2+1))-(p./((f-w).^2+1));

I evaluated the function over the variables f, w and p. Now I want find the 3db-bandwidth of resulting spectrum over certain values of f, lets say(f1= -0.5,f2=0.5) * only* and not over the entire period. Afterwards, I want to plot the bandwidth against p and w , and find the SNR Thank you

   N = 200 ;

    f = linspace(-4,4,N) ;

    p = linspace(0,1,N) ;

    w = linspace(0,2,N) ;

    [f,p,w] = meshgrid(f,p,w) ;

    y=(1./((f.^2)+1))-(p./((f+w).^2+1))-(p./((f-w).^2+1));