1. We are asked to evaluate the function $f(x) = \frac{x + 1}{2x^2 - x - 3}$ at $x = -1$. 2. The formula for the function is given as: $$f(x) = \frac{x + 1}{2x^2 - x - 3}$$ 3. To find $f(-1)$, substitute $x = -1$ into the function: $$f(-1) = \frac{-1 + 1}{2(-1)^2 - (-1) - 3}$$ 4. Simplify the numerator: $$-1 + 1 = 0$$ 5. Simplify the denominator step-by-step: $$2(-1)^2 - (-1) - 3 = 2(1) + 1 - 3 = 2 + 1 - 3 = 0$$ 6. So the function value is: $$f(-1) = \frac{0}{0}$$ 7. Since the expression results in an indeterminate form $\frac{0}{0}$, we need to simplify the function before substituting. 8. Factor the denominator: $$2x^2 - x - 3 = (2x + 3)(x - 1)$$ 9. The numerator is $x + 1$, which does not factor with the denominator factors, so no common factors to cancel. 10. Since direct substitution leads to $\frac{0}{0}$, the function is undefined at $x = -1$. **Final answer:** $f(-1)$ is undefined because the denominator is zero at $x = -1$ and the function has a discontinuity there.