Let f(x) is a function continuous for al...

Let f(x) is a function continuous for all `x in R` except at x = 0 such that `f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo)`. If `lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5`, then the image of the point (0, 1) about the line, `y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x)`, is

A

`((12)/(25),(-9)/(25))`

B

`((12)/(25),(9)/(25))`

C

`((16)/(25),(-8)/(25))`

D

`((24)/(25),(-7)/(25))`

Verified by Experts

The correct Answer is:

D

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