A) 3
B) \[-4\]
C) 5
D) None of the above
Correct Answer: D
Solution :
Given, \[f\left( \frac{3x-y}{2} \right)=\frac{3f(x)-f(y)}{2}\] \[\Rightarrow \] \[f\left( \frac{3x-y}{3-1} \right)=\frac{3f(x)-f(y)}{3-1}\]which satisfies section formula for abscissa on LHS and ordinate on RHS. Hence,\[f(x)\]must be the linear function (as only straight line satisfies such section formula). Hence, \[f(x)=ax+b\] But \[f(0)=2\Rightarrow b=2,r(0)=1\] \[\Rightarrow \] \[a=1\] Thus, \[f(x)=x+2\] \[\therefore \] \[f(2)=4\]You need to login to perform this action.
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