how do i do this?

Question

f(1/x)=x+sqrt(1+x²) find f(x)

 

Answer 1

f(1/x) = x + √(1+x²)

 

To find f(x), just replace 1/x with x.  Note that x is the inverse of 1/x and that x = 1/(1/x):

 

f(1/x) = (1/(1/x)) + √(1+(1/(1/x))²)          [Re-wrote x as 1/(1/x)]

 

So f(x) = (1/x) + √(1+(1/x)²)                   [Replace the 1/x's with x]

Which simplifies to:

 

f(x) = (1/x) + (1/x)√(1+x²)