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Question

If f(x)=x1x2 and f(1)=12 then find f(x).

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Solution

Given,
f(x)=x1x2
Integrating both sides we get,
f(x)=x22+1x+c [ Where c is integrating constant]
Given f(1)=12.
or, 12=12+1+c
or, c=1
Using value of c we have,
f(x)=x22+1x1.

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