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Let f:[0,1] to [0,1/2] be a function suc...

Let `f:[0,1] to [0,1/2]` be a function such that `f(x)` is a polynomial of 2nd degree, satisfty the following condition :
(a) `f(0)=0`
(b) has a maximum value of `1/2 at x=1`.
If A is the area bounded by `y=f(x)=f^(-1)(x)` and the line `2x+2y-3=0` in 1st quadrant, then the value of 24A is equal to `"......"`.

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