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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 c ne b`

B

`a=c and a ne b`

C

`a ne b and c ne b`

D

`a=b=c`

Text Solution

Verified by Experts

The correct Answer is:
D
Given function, `f(x)=x^(x^(2))+e^(-x^(2)),g(x)=xe^(x^(2))+e^(-x^(2)) and h(x)=x^(2)e^(x^(2))+e-x^(2)` are stricctly increasing on [0,1].
Hence, at x=1,
the given function, attains absolute maximum all equal to e+1/e.
`rArr a=b=c`
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