Question

how to solve questions like
f(1)=2
f(2)=6
f(3)=12
f(4)=?

Answer 1

you didn't mention about which type of equation . by the way
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let f(x ) = ax² + bx + c

put
f(1) =a + b + c = 2 --------(1)
f(2) =4a +2b + c = 6--------(2)
f(3) =9a +3b + c = 12 -------(3)

now, by equation (1) and (2)
3a +b = 4 ------(4)
by equation (2) and(3)
5a + b = 6 ------(5)
solve equations (4) and (5)
a = 1 and b = 1
put this in equation (1) c = 0

then equation is
f(x) = x² + x
hence,
f(4) = 16 +4 = 20
hence answer is f(4) = 20

Answer 2

hope this answer helps u please mark it as brainlest