Find the F(x) based on given points

Question

Find an equation that satisfies the given sequence

x | f(x)

1 | 2

2 | 4

3 | 6

4 | $π$

Normally, I would solve this myself but the f(4) = $π$ has really got me stumped

Answer 1

$f(x)=2x$ if $x\neq4$ and $f(4)=\pi$

Answer 2

Hint. There are any number of answers to this, but perhaps you could try $$f(x)=2x+c(x-1)(x-2)(x-3)\ .$$ If you find the right value of $c$ it will work.

Answer 3

Easily generalised:

$f(x)=2\frac{(x-2)(x-3)(x-4)}{(1-2)(1-3)(1-4)}+4\frac{(x-1)(x-3)(x-4)}{(2-1)(2-3)(2-4)}+6\frac{(x-1)(x-2)(x-4)}{(3-1)(3-2)(3-4)}+\pi\frac{(x-1)(x-2)(x-3)}{(4-1)(4-2)(4-3)}$