Question

HELP: Show that F(x)=x+x^-1 is one to one on the interval {1, infinity) and find the inverse of F^-1(x)!!!!!!!!!!!!!!!!

Answer 1

If you graph the function, you can see that the function approaches a line on the interval (1, infinity)

Answer 2

yeah but how do you find the inverse of the formula??

Answer 3

Switch x and y in the function and then solve for y. So y=x+x^-1 becomes x=y+y^-1 and then just solve the equation for y.

Answer 4

probably would help to write it as
\[f(x)=x+\frac{1}{x}=\frac{x^2+1}{x}\]

Answer 5

then solve
\[x=\frac{y^2+1}{y}\] for \(y\)
it will require solving a quadratic equation, so could be a bit tricky

Answer 6

you know how to do that, or you need help?

Answer 7

yes!!! thank you!!!1 makes sense