Find the composite function (f ext o g)(x) given f(x) = x2 − 1 and g(x) = sqrt(x) + 1.

We have $f(x) = x^2 - 1$ and $g(x) = \sqrt{x} + 1$.

The notation $(f \circ g)(x)$ means $f(g(x))$.
Substitute $g(x)$ into the expression for $f(x)$:

Replace $x$ in $f(x)$ with $(\sqrt{x} + 1)$:

Expand $(\sqrt{x} + 1)^2$ using the formula $(a+b)^2 = a^2 + 2ab + b^2$:

The simplified expression is $x + 2\sqrt{x}$. This matches option A.

The final answer is $\text{A. } x + 2\sqrt{x}$.