# How do I find x for a given value of y?

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Dan Teep on 7 Nov 2013
Commented: Brian Wilkinson on 17 Dec 2021
I'm stuck on this, and no one seems to understand the question. I've defined several variables and made x an array of values. I then made an anonymous function and used fplot to graph it's outputs(F in this case) for every x value. Now, I just need to find the x value that give me F=90. The only way I can think to do it is to solve for x by hand and then type that into matlab but there has to be a simpler way. Any body know how to do this? Here's up to where I'm stuck:
% Clear all windows and variables
clc
% Input the values for mass, height, friction coefficient, and gravity
m=18; % Mass (kilograms)
h=10; % Height (meters)
mu=0.55; % Friction coefficient (no units)
g=9.81; % Gravitational acceleration (m/s^2)
% Input a reasonable range for x
x=[-100:100];
% Calculate F given the range of x
F=@(x) (mu.*m.*g.*(h.^2 + x.^2).^(1/2))/(x+mu.*h);
% Plot F as a function of x
fplot(F,[0,100])
title('Force versus Distance')
xlabel('Distance (meters)')
ylabel('Force (newtons)')
grid on
% Find the x value that gives F=90
??????????????
Brian Wilkinson on 17 Dec 2021
Here is a code I created that solves for x given y.
% This code solves for x given a value of y. Just set the value for x_low,
% x_high, and y. Enter the formula in terms of x inside the for loop and
% set it equal to y_i.
x_low=-100; %the lowest value of x that the for loop could possibly output
x_high=100; %the highest value of x that the for loop could possibly output
y=90; %known value of y
x=(x_low+x_high)/2;
for i=1:1000
m=18; % Mass (kilograms)
h=10; % Height (meters)
mu=0.55; % Friction coefficient (no units)
g=9.81; % Gravitational acceleration (m/s^2)
y_i=(mu.*m.*g.*(h.^2 + x.^2).^(1/2))/(x+mu.*h);
if y_i<y %the greater than or less than sign may need to be flipped to get a correct value of x after the for loop completes
x=x-((x_high-x_low)/(2^(i+1)));
else
x=x+((x_high-x_low)/(2^(i+1)));
end
end
fprintf('x= %f',x)

Image Analyst on 7 Nov 2013
Fx = (mu.*m.*g.*(h.^2 + x.^2).^(1/2)) ./ (x+mu.*h);
% Plot the function.
figure;
plot(x, Fx, 'b-');
grid on
% Find the x value that gives F=90.
% This happens when the difference between Fx and 90 is a minimum.
[difference, index_At_F_Equals_90] = min(abs(Fx-90))
% Get the x value at that index. Print to command window.
x90 = x(index_At_F_Equals_90)
Kalyan Dash on 6 Feb 2018
Thanks Walter. It is much clear now after reading the description. I have used it in my code and it worked.

Walter Roberson on 7 Nov 2013
Edited: Walter Roberson on 7 Nov 2013
fzero((x) F(x)-90, [0, 100])
##### 2 CommentsShowHide 1 older comment
Walter Roberson on 7 Nov 2013
Darn, somehow I deleted a character
fzero(@(x) F(x)-90, [0, 100])

Deep Patel on 29 Mar 2018
how to solve 4*exp(-x^2)*sin(x) = 1 for x in matlab?
Deep Patel on 29 Mar 2018
Thank you very much