Question: Need help about the command of curve fitting

I have an implicit relation in lambda and x, so I am unable to find the value of x in terms of lambda so I generate a set of data points for different values of  x=0,0.1...0.9 and obtained the value of lambda. so my question is how to write a polynomial in terms of lambda for generated data by using curve fitting and how do I checked that the obtained polynomial is correct? pls have look at my maple sheet
 

restart

``

lambda1 := -(3*(-6.003*(1+(1/2)*x^2)^3+15.400672*(1+(1/2)*x^2)^2-8.745236204-7.393580208*x^2))/(20*(1+(1/2)*x^2)^4)

-(3/20)*(-6.003*(1+(1/2)*x^2)^3+15.400672*(1+(1/2)*x^2)^2-8.745236204-7.393580208*x^2)/(1+(1/2)*x^2)^4

(1)

lambda := x -> -1/20*(3*(-1)*6.003*(1 + 1/2*x^2)^3 + 3*15.400672*(1 + 1/2*x^2)^2 + 3*(-8.745236204) + 3*(-1)*7.393580208*x^2)/(1 + 1/2*x^2)^4

proc (x) options operator, arrow; -(1/20)*((-3)*6.003*((1+(1/2)*x^2)^3)+3*15.400672*((1+(1/2)*x^2)^2)+(-3)*8.745236204+(-3)*7.393580208*(x^2))/(1+(1/2)*x^2)^4 end proc

(2)

``

data := [[-0.9786536940e-1, 0], [-0.9445602756e-1, .1], [-0.8473253146e-1, .2], [-0.7004169606e-1, .3], [-0.5215959008e-1, .4], [-0.3283205398e-1, .5], [-0.1345044656e-1, .6], [0.5065808031e-2, .7], [0.2221891323e-1, .8], [0.3780341349e-1, .9], [0.5177568628e-1, 1.0]]

[[-0.9786536940e-1, 0], [-0.9445602756e-1, .1], [-0.8473253146e-1, .2], [-0.7004169606e-1, .3], [-0.5215959008e-1, .4], [-0.3283205398e-1, .5], [-0.1345044656e-1, .6], [0.5065808031e-2, .7], [0.2221891323e-1, .8], [0.3780341349e-1, .9], [0.5177568628e-1, 1.0]]

(3)

``


 

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