Inverse Lagrange Interpolation | UPSC ISS 2020 Paper-1 | Problem-69 | RitwikMath

Learn how to find the value of \(x\) corresponding to a given function value using Inverse Lagrange Interpolation in this Numerical Analysis PYQ solution. In this video, we interpolate \(x\) as a function of \(y\) and estimate the required value step-by-step.

Perfect for students preparing for UPSC Statistics Optional, ISS, CSIR NET, GATE, IIT JAM, and other mathematics/statistics competitive exams.

📌 Problem Covered:
Find the approximate value of:
\[
x
\]
for which:
\[
f(x)=15
\]

📌 Method Used:
Since the value of:
\[
y=f(x)
\]
is given and we need to determine:
\[
x
\]
we use:
### Inverse Lagrange Interpolation Formula

📌 Formula:
:contentReference[oaicite:0]{index=0}

📌 Substituting the Given Data:
Using the interpolation points and evaluating at:
\[
y=15
\]

the computation gives:
\[
x(15)\approx10.5
\]

📌 Final Answer:
:contentReference[oaicite:1]{index=1}

📌 Concepts Explained:
- Inverse Interpolation
- Lagrange Interpolation Formula
- Function Approximation
- Unequally Spaced Data
- Numerical Analysis PYQ
- Polynomial Interpolation

🎯 Useful For:
- UPSC Statistics Optional
- ISS Exam
- CSIR NET Mathematical Sciences
- GATE Mathematics
- IIT JAM
- Engineering Mathematics
- Applied Mathematics Students

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