Answer
$(f \circ f)(x) = 101$
Work Step by Step
We can rewrite $(f \circ f)(x)$ as $f(f(x))$. This means that we evaluate the inner function, $f(x)$, first. Then we use the result of $f(x)$ and plug it into the outer function, which is also $f(x)$.
Plug $3$ into the inner function, $f(x)$, and evaluate:
$(f \circ f)(3) = f(f(3)) = 3^2 + 1$
Multiply to simplify:
$(f \circ f)(3) = f(f(3)) = 9 + 1$
Add to simplify:
$(f \circ f)(3) = f(f(3)) = 10$
Plug this result into the outer function, $f(x)$:
$f(10) = (10)^2 + 1$
Evaluate the exponential term first:
$f(10) = 100 + 1$
Add to simplify:
$f(10) = 101$
