Let `f={(-1,-3),(0,-1),(1,1),(2,3)}` be a function, described by the f – InterviewSolution

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1.	Let `f={(-1,-3),(0,-1),(1,1),(2,3)}` be a function, described by the formula, `f(x)=alphax+beta`. Then, find the valves of `alphaandbeta`. Also, find the formula.
Answer» Here `f(x)=alphax+beta" "....(i)` Also, `f(-1)=-3,f(0)=-1,f(1)=1andf(2)=3." "["given"]` Putting `x=-1andf(-1)=-3` in (i), we get `-alpha+beta=-3impliesalpha-beta=3" "....(ii)` Putting `x=0andf(0)=-1` (i), we get `alphaxx0+beta=-1impliesbeta=-1" "....(iii)` Putting `beta=-1` from (iii), in (ii), we get `alpha=2`. `:.alpha=2andbeta=-1`. Hence, `f(x)=2x-1` is the required formula.

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