wolfram alpha operation in matlab

how can i enter an expression and get the value of the variable that creates it?(like in wolfram alpha attached photo)

Thanks

Answer 1

[Walter Roberson]

Alternately,

syms x
solve(1.08393 == (1+x)/(1-x), x)

[fima v]

is there a way do it on a whole vector instead of 1.08393' i get an error

Thanks

Warning: The solutions are valid under the following conditions: z - 1 ~= 0 & z == 186134054074199/2437933867759447 & z == 2374416420871865/11381615675612857 & z == 3937943466562597/8441543093933093 & z == 6495012520173245/7057962473594557. To include parameters and conditions in the solution, specify the 'ReturnConditions' option.

[Walter Roberson]

John D'Errico's solution (k - 1)./(k + 1) looks fine.

Answer 2

[Stephen23]

>> fun = @(x)(1+x)/(1-x)-1.08393;
>> fzero(fun,0)
ans =
        0.0402748652785842

Answer 3

[John D'Errico]

It seems silly to throw a computer at something that is done using pencil and paper. I think sometimes we forget how to think, allowing the computer to do that for us. That can get to be a habit, and once we lose a skill, it won't be grown again easily.

k = (1+x)/(1-x)

First, look at the plot that is most easily drawn using ezplot:

ezplot(@(x) (1+x)./(1-x))
grid on

Here we see that if we were to swap the axes, trying to produce x as function of k, we would still have a hyperbolic form.

Quick pencil and paper shows (as long as x is not 1, in which case there is no solution anyway):

x = (k-1)/(k+1)

Here we see that k may never be -1 either, in which case no solution could have existed since we would have needed to divide by zero. As I suggested, the result should again have a clearly hyperbolic form, which it does. Always check your results against your knowledge of the process. Any computation, whether done using paper or computer, should always be checked for sanity.

In MATLAB, for vector or array k, the solution is now trivial.

x_k = @(k) (k-1)./(k+1);
x_k(0:0.25:2)
ans =
          -1         -0.6     -0.33333     -0.14286            0      0.11111          0.2      0.27273      0.33333

x_k(1.08393)
ans =
     0.040275

format long g
x_k(1.08393)
ans =
        0.0402748652785842

Note the use of the ./ operator.