The domain of the function \( f(x)=...
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The domain of the function ( f(x)=exp (sqrt{5 x-3-2 x^{2}}) )
( (a)left[1,-frac{3}{2}right] )
(b) ( left[frac{3}{2}, inftyright] )
( (c)[-infty, 1] )
( (d)left[1, frac{3}{2}right] )

JEE/Engineering Exams
Maths
Solution
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( f(x)=e^{(sqrt{5 x-3-2 x^{2}}} )
( 5 x-3-2 x^{2} geqslant 0 )
( 2 x^{2}-5 x+3 leq 0 )
( x=frac{5 pm sqrt{25-24}}{4} )
( =frac{5 pm 1}{4}=frac{6}{4} ) or 1
So, option ( (d)left[1, frac{3}{2}right] ) is correct answer.

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