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Let f(x) polynomial of degree 5 with lea...

Let f(x) polynomial of degree 5 with leading coefficient unity such that f(1)=5, f(2)=4,f(3)=3,f(4)=2,f(5)=1, then f(6) is equal to

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Let `f(x)=g(x)-x+6`
`f(1)=5 =>g(1)=0`
`f(2)=4 =>g(2)=0`
`f(3)=3 =>g(3)=0`
`f(4)=2 =>g(4)=0`
`f(5)=1 =>g(5)=0`
therefore g(x) is a function such that `g(x)=(x-1)(x-2)(x-3)(x-4)(x-5)`
therefore `f(x)=(x-1)(x-2)(x-3)(x-4)(x-5)-x+6`
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