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Let f(x) be defined for all x > 0 and be...

Let f(x) be defined for all x > 0 and be continuous. `Let f(x) satisfy f((4x)/y)=f(x)-f(y) for all x,y and f(4e) = 1, then `
`(a) f(x) = In 4x(b) f(x) is bounded (c) lim_(x->0) f(1/x)=0 (d) lim_(x->0)xf(x)=0`

Text Solution

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`(9x^2-64)/(x-1-(1/(1-(x/(4+x))))`
`=((3x)^2-(8)^2)/(x-1-(1/((4+x-x)/(4+x)))`
`=((3x+8)(3x-8))/(x-1-((4+x)/4)`
`=((3x+8)(3x-8))/((4x-4-4-x)/4)`
`=4(3x+8)=12x+32`
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