Answer:
Domain of n^-1(x) = x ≤ -2 or x ≥ 2
Explanation:
We begin by finding the inverse of the function n(x).
n(x) = x + 1/x
To find the inverse, we replace n(x) with y:
y = x + 1/x
Then we solve for x in terms of y:
yx = x^2 + 1
x^2 - yx + 1 = 0
Using the quadratic formula, we get:
x = (y ± √(y^2 - 4))/2
Therefore, the inverse function of n(x) is:
n^-1(x) = (x ± √(x^2 - 4))/2
The domain of n^-1(x) is all values of x that make the expression under the square root non-negative:
x^2 - 4 ≥ 0
(x - 2)(x + 2) ≥ 0
The expression is non-negative when x ≤ -2 or x ≥ 2. Therefore, the domain of n^-1(x) is:
Domain of n^-1(x) = x ∈ R