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Q.
If $f ( x )$ is a monic polynomial function of degree 4 satisfying $f ( i )=\frac{1}{ i }$ for $i =1,2,3,4$ then
Relations and Functions - Part 2
Solution:
$ x f( x )-1 \equiv( x -1)( x -2)( x -3)( x -4)( x -\alpha)$
Put $x=0 \Rightarrow \alpha=\frac{1}{24}$
$\therefore f ( x )=\frac{( x -1)( x -2)( x -3)( x -4)\left( x -\frac{1}{24}\right)+1}{ x } $
$\Rightarrow f (5)=\frac{4 \times 3 \times 2 \times 1 \times \frac{119}{24}+1}{5}=24$
Now verify the options