The problem defines a piecewise function $f(x)$. $f(x) = x^2 + 1$ if $x < 1$ and $f(x) = 3x - 1$ if $x \ge 1$. We need to find the value of $f(-1)$.

1. Problem Description

The problem defines a piecewise function $f(x)$.

$f(x) = x^2 + 1$ if $x < 1$ and $f(x) = 3x - 1$ if $x \ge 1$.

We need to find the value of $f(-1)$.

2. Solution Steps

Since we are looking for $f(-1)$, we need to determine which part of the piecewise function applies to $x=-1$.

Because $-1 < 1$, we use the first expression for $f(x)$, which is $f(x) = x^2 + 1$.

Now, substitute $x = -1$ into the expression:

$f(-1) = (-1)^2 + 1$

$f(-1) = 1 + 1$

$f(-1) = 2$

3. Final Answer

The final answer is (d) $f(-1) = 2$.