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

JEE/Engineering Exams
Maths
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( 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) )
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