Hi,

It's a straight forward question.

Given,

x is positive and y = x^2 + 1

y = x^2 +1

x^2 = y-1

x = sqrt(y-1)

So the answer is D.

OR

We can try numbers too.

If x = 1 then y = 2.

When we substitute y = 2 in the answer choices we should get "x" value as 1.

A. y^2 - 1 = 4 - 1 = 3. Eliminate.

B. y^2 + 1 = 4 + 1 = 5. Eliminate.

C. √(y)− 1 = √2 - 1 = not an integer. Eliminate.

D. √(y - 1) = √(2 - 1) = 1. Hold on.

E. √(y + 1) = √(2 + 1) = 3. Eliminate.

So the answer is D.