If f is a real function satisfying f (x+1 x )=x^2+1 x^2 for all x - 0 , then write the expression for f(x).

We have,f (x+ 1 x ) = x^2+1 x Now, x^2+1 x^2 = (x+1 x )^2-2 [ (a+b)^2=a^2+b^2+2ab ] (x+1 x )= (x+1 x )^2-2 (x)=x^2-2,where |x| 2

If f is a real function satisfying f (x+1 x )=x^2+1 x^2 for all x…

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