How to find specific x values of specific y value of a plotted graph?

Hi I am plotting a transfer function magnitude with respect to omega. I am trying to find cut off frequencies which are the 1/sqrt(2) values of magnitude plot. So in summary I want to find x values which f(x)= 1/sqrt(2) in the graph I plotted. And if possible I want to emphasize them (by marking, crossing etc.)

I tried to find intersection point between line y=1/sqrt(2) But couldn't find a precise result as well so a follow up question. Can I find the points which 2+ plot intersected ?

Here is my code and graph

y = linspace(0,50000,50001);
R=33*10^3;
C=10^-8;
H = @(y) (R./(R-(1j./(y.*C))));
figure;
subplot(2,1,1);
plot(y,abs(H(y)));
xlabel('\omega'); 
ylabel('|H(j\omega)|');
hold on;
yline(1/sqrt(2));

Answer 1

[KSSV]

y = linspace(0,50000,50001);    % y values 
R=33*10^3;                      % constant 
C=10^-8;                        % constant 
H = @(y) (R./(R-(1j./(y.*C)))); % function

val = abs(H(y)) ;               % evaluate absolute function H values at y 
vali = 1/sqrt(2) ;              % the value of val (y-axes) at which y (x-axes_ to be sought 
yi = interp1(val,y,vali) ;      % do interpolation to get respective y-value ofr given vali

figure;
plot(y,val);
xlabel('\omega'); 
ylabel('|H(j\omega)|');
hold on;
yline(1/sqrt(2));
plot(yi,vali,'*r')

[Utku Deniz Altiok]

Thanks a lot but a functionality explanation as a %comment near the lines would be wonderful

[KSSV]

done..

[Utku Deniz Altiok]

Is there any more simpler method than interpolation? since its not a concept I am familiar with

[KSSV]

y = linspace(0,50000,50001);    % y values 
R=33*10^3;                      % constant 
C=10^-8;                        % constant 
H = @(y) (R./(R-(1j./(y.*C)))); % function

val = abs(H(y)) ;               % evaluate absolute function H values at y 
vali = 1/sqrt(2) ;              % the value of val (y-axes) at which y (x-axes_ to be sought 

yi = y(abs(val-vali)<10^-3) ;   % Get the index in val where val == vali 

figure;
plot(y,val);
xlabel('\omega'); 
ylabel('|H(j\omega)|');
hold on;
yline(1/sqrt(2));
plot(yi,vali,'*r')