Question

if $f(3)$ =5 and $f(5)$ =3, what is the form of $f(x)$ by lagrange's formula

Answer 1

Lagrange First Order Interpolation Formula

$$f(x) = f(x_0)+(x − x_0)\dfrac{f(x_0) − f(x_1)}{x_0 − x_1}$$

Given $x_0=3, f(x_0)=f(3)=5,$

$x_1=5, f(x_1)=f(5)=3$

Then

$$f(x) = 5+(x − 3)\dfrac{5-3}{3-5}$$

$$f(x) = 5-(x − 3)$$

$$f(x) =-x+8$$