Let \( f, g \) and \( h \) be real-valued functions defined on the interval \( [0,1] \) by \( f(...

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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
[One Correct Option, 2010]
(a) \( a=b \) and \( c \neq b \)
(b) \( a=c \) and \( a \neq b \)
(c) \( a \neq b \) and \( c \neq b \)
(d) \( a=b=c \)
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