CircleHard

Question

If 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) + 1
put 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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