Question

If g(x) is a polynomial satisfying

g(x) g(y) = g(x) + g(y) + g(xy) –2 for all real x and y and g(2) = 5, then $\lim_{x \rightarrow 3}$g(x) is-

• A. –8
• B. 10
• C. 8
• D. None of these

Answer 1

Answer: (B)

10

Answer 2

Put x = 2, y = 1

g (2) g(1) = g(2) + g(1) + g(2) –2

g (1) = 8 (Q g(2) = 5)

g(1) = 2

Put y = 1/x

g(x). g(1/x) = g(x) + g(1/x) \ g(x) = xⁿ + 1

g(2) = 2ⁿ + 1 Ž 5 = 2ⁿ + 1

\ n = 2 \ g(n) = n² + 1

$\lim_{x \rightarrow 3}$ (x² +1) = 3² + 1 = 10