Composite Functions

If f(x) = √(x³), then f(3x) will be equal to

Direction for Question 2 to 4: Read the instruction below and solve.

f(x) = f(x – 2) – f(x – 1), x is natural number f(1) = 0, f(2) = 1

Q. The value of f(8) is

Direction for Question 2 to 4: Read the instruction below and solve.

f(x) = f(x – 2) – f(x – 1), x is natural number f(1) = 0, f(2) = 1 

Q. The value of f(7) + f(4) is

What will be the value of ∑f(n) (where n= 1 to 9) ?

Directions for Questions 5 to 9: Define the following functions:

(i) a @ b = (a + b) / 2

(ii) a # b = a² – b²

(iii) (a ! b) = (a – b) / 2

Q. Find the value of {[(3@4)!(3#2)] @ [(4!3)@(2#3)]}.

Directions for Questions 5 to 9: Define the following functions:

(i) a @ b = (a + b) / 2

(ii) a # b = a² – b²

(iii) (a ! b) = (a – b) / 2

Q.  Find the value of (4#3)@(2!3).

Directions for Questions 5 to 9: Define the following functions:

(i) a @ b = (a + b) / 2

(ii) a # b = a² – b²

(iii) (a ! b) = (a – b) / 2

Q.  Which of the following has a value of 0.25 for a = 0 and b = 0.5?

Directions for Questions 5 to 9: Define the following functions:

(i) a @ b = (a + b) / 2

(ii) a # b = a² – b²

(iii) (a ! b) = (a – b) / 2

Q. Which of the following expressions has a value of 4 for a = 5 and b = 3?

Directions for Questions 5 to 9: Define the following functions:

(i) a @ b = (a + b) / 2

(ii) a # b = a² – b²

(iii) (a ! b) = (a – b) / 2

Q.  If we define a$b as a³ – b³, then for integers a, b > 2 and a > b which of the following will always be true?

A function F(n) is defined as F(n – 1) = 1/(2 – F(n)) for all natural numbers ‘n’. If F(1) = 3, then what is the value of [F(1)] + [F(2)] + … + [F(1000)]? (Here, [x] is equal to the greatest integer less than or equal to x)