CircleHard
Question
If 
2f(tx)dt = f(x) +1, where f(x) is non constant function, then y = f(x) represents -
2f(tx)dt = f(x) +1, where f(x) is non constant function, then y = f(x) represents -Options
A.family of parallel lines
B.family of lines with constant y intercept
C.family of circles centred at origin
D.family of circles with radius unity
Solution
2f(tx) dt = f(x) + 1put tx = z
⇒
2f(z)dz = x(f(x) + 1)⇒ 2f(x) = xf′(x) + f(x) + 1
xf′(x) = f(x) - 1
ln(f(x)- 1) = lnx + lnc
⇒ f(x) - 1 = cx ⇒ = cx + 1
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