If g(x) = x + 1 and f(x + (1)/(x)) = x2 + (1)/(x2), what is f(g(2))?

The function $g(x)$ is given by $g(x) = x + 1$.
Substitute $x=2$ into $g(x)$:

$$g(2) = 2 + 1 = 3$$

The function $f$ is defined by $f(x + \frac{1}{x}) = x^2 + \frac{1}{x^2}$.
We know the algebraic identity $(a+b)^2 = a^2 + 2ab + b^2$.
Let $a=x$ and $b=\frac{1}{x}$. Then:

$$\left(x + \frac{1}{x}\right)^2 = x^2 + 2 \cdot x \cdot \frac{1}{x} + \left(\frac{1}{x}\right)^2$$ $$\left(x + \frac{1}{x}\right)^2 = x^2 + 2 + \frac{1}{x^2}$$

Rearranging this, we get:

$$x^2 + \frac{1}{x^2} = \left(x + \frac{1}{x}\right)^2 - 2$$

So, we can rewrite the definition of $f$ as:

$$f\left(x + \frac{1}{x}\right) = \left(x + \frac{1}{x}\right)^2 - 2$$

Let $u = x + \frac{1}{x}$. Then the function $f$ can be written as $f(u) = u^2 - 2$.

From Step 1, we found $g(2) = 3$.
Now we need to find $f(3)$. Using the simplified form of $f(u)$ from Step 2:

$$f(3) = (3)^2 - 2$$ $$f(3) = 9 - 2$$ $$f(3) = 7$$

The calculated value is 7, which corresponds to option (B).

The final answer is $\text{B}$