1. The problem asks us to determine whether the function $f(x) = x^2 + 1$ is even, odd, or neither. 2. Recall the definitions: - A function is **even** if $f(-x) = f(x)$ for all $x$. - A function is **odd** if $f(-x) = -f(x)$ for all $x$. 3. Calculate $f(-x)$: $$f(-x) = (-x)^2 + 1 = x^2 + 1$$ 4. Compare $f(-x)$ with $f(x)$: $$f(-x) = x^2 + 1 = f(x)$$ 5. Since $f(-x) = f(x)$, the function $f(x) = x^2 + 1$ is an **even function**. 6. It is not odd because $f(-x) \neq -f(x)$: $$-f(x) = -(x^2 + 1) = -x^2 - 1 \neq x^2 + 1 = f(-x)$$