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Let f,g and h be real-valued functions d...

Let `f,g` and `h` be real-valued functions defined on the interval `[0,1]` by `f(x)=e^(x^2)+e^(-x^2)` , `g(x)=x e^(x^2)+e^(-x^2)` and `h(x)=x^2 e^(x^2)+e^(-x^2)`. if `a,b` and `c` denote respectively, the absolute maximum of `f,g` and `h` on `[0,1]` then

A

`a=b` and b!+c`

B

`c=a` and a!+b`

C

`a!=b` and `b!+c`

D

`a=b=c`

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