Question

( F(x)=log _{e}(sqrt{sqrt{x^{2}+1}+x}+sqrt{sqrt{x^{2}+1}-x}) )
Domain, ( sqrt{sqrt{x^{2}+1}+x}+sqrt{sqrt{x^{2}+1}-x}>0 )
( Rightarrow sqrt{sqrt{x+1}+x}>sqrt{sqrt{x^{2}+1}-x} )
Sequaring both sides wr get ( Rightarrow(sqrt{sqrt{x+1}+x})^{2}>(sqrt{x^{2}+1}-x)^{2} )
( Rightarrow quad sqrt{x+1}+x>sqrt{x^{2}+1}-x )
( Leftrightarrow quad x>-x )
( Rightarrow quad 2 times, 0 )
( Rightarrow quad x>0 )
( x in(0, infty) )

# Example 96 The function f :R → defined as f(x)=loge (VVx2 +1+x+V/XP+1- x) is

Solution