CAT Question Bank  Functions

Q21) f(x) = x + 1/x
[f(x)]^3 = f(x^3) + kf(1/x)
k = ?
a) 1
b) 3
c) 3
d) 1

Q22) f(x) is a 4 degree polynomial satisfying f(n) = 1/n for integers n = 1 to 5.
If f(0) = a/b, where a and b are coprime positive integers. What is the value of a + b ?

Q23) If f(f(x)) = x^4 + 4x^3 + 4x^2  2, then f(2) = ?
a. 2
c. 0
c. 7
d. 1
e. None of the above

Q24) If f(x) is cubic polynomial with coefficient of x^3 as 1. It is given that it has nonnegative real roots and f(0) = 64. Find the largest possible value of f(1).

Q25) f(x) is a cubic Polynomial with leading coefficient as 1.
If f(1) = 11
f(2) = 104
f(3) = 1027.
Find the value of f(0).
a) 4
b) 5
c) 6
d) 7

Q26) Range of f(x) = 1/√(x  [x]) ?

Q27) Let f(x) = 4x^3 + 21x^2 + 41x + 24 be identical to g(x) = a(x+2)^3 + b(x+2)^2 + c(x+2) + d
Find a  b + c  d

Q28) f(xy) = f(x) + f(y) ‐ 2. If f(2) = a and f(3) = b, then the value of f(72) is:
a) a + b ‐ 2
b) 2a + 2b ‐ 6
c) 2a + 3b ‐ 8
d) 3a + 2b ‐ 8

Q29) A function ƒ(x) satisfies ƒ(1) = 3600 and ƒ(1) + ƒ(2) + ... + ƒ(n) = n2 f(n), for all positive integers n > 1. What is the value of ƒ(9)?

Q30) f(xy) = f(x)f(y) for all real values of x and y, and f(2)=1/8.
Find the value of f(1) + f(1/2) + f(1/3)
a) 11/6
b) 1/6
c) 6
d) 36


@rowdyrathore 3/8

@rowdyrathore 100


@rowdyrathore k=3


@rowdyrathore f(6)=1 * 4 * 9 * 16 * 25 * 36 / 720

@rowdyrathore 34/3

@SoumyaRanjanPatra How you got this value ? Answer is 720 + 7^2
f(x) = (x + 1)^2 for x = [0, 5]
Also, as f(x) has a degree six with coefficient of x^6 as 1, we can write
f(x) = x (x  1) (x 2) (x  3) (x  4) (x  5) + (x + 1)^2
so f(6) = 6 * 5 * 4 * 3 * 2 * 1 + 7^2
f(6) = 720 + 7^2

Method 1 :
2f(x) + f(1 – x) = x^2
2f(5) + f(4) = 25 (for x = 5)  (1)
2f(4) + f(5) = 16 (for x =  4)  (2)
Solve for f(5)  (1) * 2  (2)
3f(5) = 50  16 = 34
f(5) = 34/3Method 2 : [Solution by @vikas_saini ]
2f(x) + f(1  x) = x^2
2f(1  x) + f(x) = (1x)^2
3f(x) = 2x^2  (1x)^2
x = 5
3 f(5) = 34
f(5) = 34/3