Question

Select the correct answer.

Answer 1

Answer:

$(c)\ f(5) < g(3)$

Step-by-step explanation:

Given

$f(n) = 2(n-1) -1$

$g(n) = 3n + 6$

Required

Which is correct

$(a)\ g(6) < f(6)$

Calculate g(6) and f(6)

$f(n) = 2(n-1) -1$

$f(6) = 2(6 - 1) -1 = 2*5-1=9$

$g(n) = 3n + 6$

$g(6) =3*6 +6 =24$

(a) is false, because g(6) > f(6) i.e. 24 > 9

$(b)\ f(7) > g(10)$

Calculate f(7) and g(10)

$f(n) = 2(n-1) -1$

$f(7) = 2*(7-1)-1=2*6-1=11$

$g(n) = 3n + 6$

$g(10) =3*10+6=36$

(b) is false, because f(7) < g(10) i.e. 11 <36

$(c)\ f(5) < g(3)$

Calculate f(5) and g(3)

$f(n) = 2(n-1) -1$

$f(5) =2 *(5-1)-1 = 2*4-1=7$

$g(n) = 3n + 6$

$g(3) = 3*3+6=9+6=15$

(c) is true, because f(5) < g(3) i.e. 7 <15