Let g(x) be a function satisfying g(0)=2,g(1)=3,g(x+2)=2g(x)-g(x+1), then find g(5)

Asked by Anil | 10th May, 2017, 08:05: PM

Expert Answer:

begin mathsize 16px style straight g left parenthesis 0 right parenthesis equals 2 comma straight g left parenthesis 1 right parenthesis equals 3 comma straight g left parenthesis straight x plus 2 right parenthesis equals 2 straight g left parenthesis straight x right parenthesis minus straight g left parenthesis straight x plus 1 right parenthesis
rightwards double arrow straight g left parenthesis 2 right parenthesis equals 2 straight g left parenthesis 0 right parenthesis minus straight g left parenthesis 1 right parenthesis space space space space space space space open parentheses space here space straight x equals 0 space in space straight g left parenthesis straight x plus 2 right parenthesis equals 2 straight g left parenthesis straight x right parenthesis minus straight g left parenthesis straight x plus 1 right parenthesis close parentheses
rightwards double arrow straight g left parenthesis 2 right parenthesis equals 2 cross times 2 minus 3
rightwards double arrow straight g left parenthesis 2 right parenthesis equals 1
Thus comma space space find space straight g left parenthesis 3 right parenthesis comma straight g left parenthesis 4 right parenthesis.
rightwards double arrow straight g left parenthesis 3 right parenthesis equals 2 straight g left parenthesis 1 right parenthesis minus straight g left parenthesis 2 right parenthesis space equals 5
rightwards double arrow straight g left parenthesis 4 right parenthesis equals 2 straight g left parenthesis 2 right parenthesis minus straight g left parenthesis 3 right parenthesis space equals negative 3
rightwards double arrow straight g left parenthesis 5 right parenthesis equals 2 straight g left parenthesis 3 right parenthesis minus straight g left parenthesis 4 right parenthesis space equals 13
end style

Answered by Sneha shidid | 11th May, 2017, 10:39: AM