We are given the functions:

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

$g(x) = 4x - 3$

We need to find $f(f(-1))$.

Step 1: Compute $f(-1)$

Substituting $x = -1$ into $f(x)$:

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

Step 2: Compute $f(f(-1)) = f(2)$

Now, we substitute $x = 2$ into $f(x)$:

$f(2) = 2^2 + 1 = 4 + 1 = 5$

Final Answer:

$f(f(-1)) = 5$

Would you like a more detailed breakdown or have any questions?

Here are five related questions for practice:

1. Find $g(g(2))$.
2. Compute $f(g(1))$.
3. Find $g(f(0))$.
4. Solve for $x$ if $f(x) = g(x)$.
5. Determine $f(g(-2))$.

Tip: When working with composite functions, always evaluate the inner function first before substituting into the outer function!