Topic - Functions

Answer key available? - No

Source - Curated Content ]]>

Topic - Functions

Answer key available? - No

Source - Curated Content ]]>

(a) 10

(b) 17

(c) 34/3

(d) Cannot be determined ]]>

If f(1) = 0.3333333...

Find the value of f(1) + f(3) + f(5) + … up to infinity ]]>

a) f(x + y)

b) f(1 + xy)

c) (x + y) f(1 + xy)

d) f ((x +y) / (1+xy)) ]]>

a) for any two real numbers x and y, f(x + y) = x + f(y)

b) f(0) = 2

What is the value of f(98) ? ]]>

F(1) = 1

F(2) = 3

F(3) = 5

F(4) = 7

F(5) = 9

Find F(6) ]]>

f(7) = 2f(5) and 5 is one of the root of f(x) = 0.

Find a + b + c ]]>

f(1) + f(2) + f(3) + ... + f(p) = p^2 × f(p)

If f(1) = 2009, then what is the value of f(2008)? ]]>

f(4) = 6

Find f(6). ]]>

f(6) + f(8) = 0

f(7).f(9) > 0

f(6).f(10) < 0

f(0) > 0 and f(1) < 0

How many of the following statements must be true?

I. f(1).f(2).f(3) < 0

II. f(3).f(5).f(7).f(9) > 0

III. f(7).f(8) < 0

IV. f(0) + f(1) + f(9) + f(10) > 0

(a) 1

(b) 2

(c) 3

(d) 4

indicates a root lies between 6 and 8

f(7).f(9) > 0

indicates f7 and f9 lie on the same side of the X axis

So, we can say

(a) root lies bw 6 and 7, and both 7 and 9 are either +ve or negative

f(6)f(10) 0 and f(1) < 0

indicates a root lies between 0 and 1

f(x) = 0 only for two distinct real values of x << Only two distinct roots. Both have been discovered.

f(0) > 0

hence it begins as a curve above the X axis, somewhere between (0,1) has a root, then becomes -ve. The second root arrives between (6,7) and beyond this curve again becomes +ve

So

I. f(1).f(2).f(3) < 0 << All three values are negative. Hence, true

II. f(3).f(5).f(7).f(9) > 0 << f3,f5 are -ve whereas f7,f9 are +ve Hence true

III. f(7).f(8) < 0 << Both are +ve hence false

IV. f(0) + f(1) + f(9) + f(10) > 0 << f0,f9,f10 are +ve while f1 is -ve

However it being a continuous curve with two roots, it cannot be predicted what will be the negative value. so not a "must be true" statement.

So ans 2

[Credits : @hemant_malhotra]

a) can not be determined

b) 7

c) -8

d) either 7 or -8

e) none of these ]]>

[f(x)]^3 = f(x^3) + kf(1/x)

k = ?

a) 1

b) 3

c) -3

d) -1 ]]>

If f(0) = a/b, where a and b are coprime positive integers. What is the value of a + b ? ]]>

a. 2

c. 0

c. 7

d. 1

e. None of the above ]]>