Question # The domain of the function ( f(x)=exp (sqrt{5 x-3-2 x^{2}}) )

# 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] )

Solution

( 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.