Answer:
1) f(x) = x² + 1
a. f(3) = 3² + 1 = 9 + 1 = 10
b. f(-1) = (-1)² + 1 = 1 + 1 = 2
2) f(1) = -2
f(n) = 2f(n - 1) + 1 for n≥2
a. f(2) = 2f(1) + 1 = 2(-2) + 1 = -4 + 1 = -3
f(3) = 2f(2) + 1 = 2(-3) + 1 = -6 + 1 = -5
f(4) = 2f(3) + 1 = 2(-5) + 1 = -10 + 1 = -9
f(5) = 2f(4) + 1 = 2(-9) + 1 = -18 + 1 = -17
b. Yes, it is possible to find f(-1).
f(1) = -2 = -1 - 1 = -2⁰ - 1
f(2) = -3 = -2 - 1 = -2¹ - 1
f(3) = -5 = -4 - 1 = -2² - 1
f(4) = -9 = -8 - 1 = -2³ - 1
f(5) = -17 = -16 - 1 = -2⁴ - 1
From these, we have:
f(n) = -(2^(n - 1)) - 1
f(-1) = -(2^-2) - 1 = -1/4 - 1 = -1 1/4