Missing term in the following table is array lllllll x & : & 0 & 1 & 2 & 3 & 4 y=f(x) & : & 1 & 3 & 9 & ? & 81 array

Step-by-step solution

Here, 4 values are given, therefore aligned ⁴ f(x)=0 x & &(E-1)⁴ f(x)=0 & (E⁴-4 E³+6 E²-4 E+1 ) f(x)=0 & E⁴ f(x)-4 E³ f(x)+6 E² f(x) -4 E f(x)+f(x)=0 & f(x+4)-4 f(x+3)+6 f(x+2) -4 f(x+1)+f(x)=0 aligned On putting x=0 , we get f(4)-4 f(3)+6 f(2)-4 f(1)+f(0)=0 ( i ) On substituting the values of f(0), f(1), f(2), f(4) in Eq. (i), we get array ll & 81-4 f(3)+6 9-4 3+1=0 & 4 f(3)=124 array f(3)=31