2. Find Solution using Lagrange's Inverse Interpolation formula

x	f(x)
2	94.8
5	87.9
8	81.3
14	68.7

x = 85
Finding f(2)

Solution:
The value of table for `x` and `y`

x	2	5	8	14
y	94.8	87.9	81.3	68.7

Lagrange's Inverse Interpolating Polynomial
The value of y at you want to find `P_n(y) : y = 85`

Lagrange's Inverse Interpolation formula is
`f(y) = ((y - y_1)(y - y_2)(y - y_3))/((y_0 - y_1)(y_0 - y_2)(y_0 - y_3)) xx x_0 + ((y - y_0)(y - y_2)(y - y_3))/((y_1 - y_0)(y_1 - y_2)(y_1 - y_3)) xx x_1 + ((y - y_0)(y - y_1)(y - y_3))/((y_2 - y_0)(y_2 - y_1)(y_2 - y_3)) xx x_2 + ((y - y_0)(y - y_1)(y - y_2))/((y_3 - y_0)(y_3 - y_1)(y_3 - y_2)) xx x_3`

`x(85) = ((85 - 87.9)(85 - 81.3)(85 - 68.7))/((94.8 - 87.9)(94.8 - 81.3)(94.8 - 68.7)) xx 2 + ((85 - 94.8)(85 - 81.3)(85 - 68.7))/((87.9 - 94.8)(87.9 - 81.3)(87.9 - 68.7)) xx 5 + ((85 - 94.8)(85 - 87.9)(85 - 68.7))/((81.3 - 94.8)(81.3 - 87.9)(81.3 - 68.7)) xx 8 + ((85 - 94.8)(85 - 87.9)(85 - 81.3))/((68.7 - 94.8)(68.7 - 87.9)(68.7 - 81.3)) xx 14`

`x(85) = ((-2.9)(3.7)(16.3))/((6.9)(13.5)(26.1)) xx 2 + ((-9.8)(3.7)(16.3))/((-6.9)(6.6)(19.2)) xx 5 + ((-9.8)(-2.9)(16.3))/((-13.5)(-6.6)(12.6)) xx 8 + ((-9.8)(-2.9)(3.7))/((-26.1)(-19.2)(-12.6)) xx 14`

`x(85) = (-0.0719) xx 2 + 0.676 xx 5 + 0.4126 xx 8 + (-0.0167) xx 14`

`x(85) = 6.3038`


Solution of the polynomial at point `85` is `x(85) = 6.3038`

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