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If f((x+2y)/3)=(f(x)+2f(y))/3AAx ,y in ...

If `f((x+2y)/3)=(f(x)+2f(y))/3AAx ,y in Ra n df^(prime)(0)=1,f(0)=2,` then find `f(x)dot`

Text Solution

Verified by Experts

The correct Answer is:
`x+2`
`"Given "f((x+2y)/(3))=(f(x)+2f(y))/(3)AAx, y in R,` which satisfies
section formula for abscissa on L.H.S. and ordinate on R.H.S. Hence, f(x) must be the linear function (as only straight line satisfies such section formula).
Hence, `f(x)=ax+b.`
But `f(0)=2rArrb=2and f'(0)=1rArra=1`.
`Thus, `f(x)=x+2.`
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