How to prepare for Quantitative Aptitude for the CAT>Chapter 20 - Functions>Level of Difficulty>Q 55

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IMPORTANT

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The function $ψ (m) = [m]$ , where $[m]$ represents the greatest integer less than or equal to $m$ . Two real numbers $x$ and $y$ are such that $ψ (4 x + 5) 5 y + 3$ and $ψ (3 y + 7) = x + 4,$ then find the value of $x^{2} \times y^{2}$ .

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Important Questions on Functions

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IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 20 - Functions>Level of Difficulty>Q 56

A certain function always obeys the rule: If

f (x . y) = f (x) . f (y)

where

x

and

y

are positive real numbers. A certain Mr. Mogambo found that the value of

f (128) = 4

, then find the value of the variable

M = f (0.5) . f (1) . f (2) . f (4) . f (8) . f (16) . ƒ (32) . f (64) . f (128) . f (256)

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How to prepare for Quantitative Aptitude for the CAT>Chapter 20 - Functions>Level of Difficulty>Q 57

x

and

y

are non negative integers such that

4 x + 6 y = 20,

and

x^{2} \leq M / y^{2 / 3}

for all values of

x, y .

What is thr minimum value of

M ?

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How to prepare for Quantitative Aptitude for the CAT>Chapter 20 - Functions>Level of Difficulty>Q 58

Let

ψ (x) = \frac{x + 3}{2}

and

θ (x) = 3 x^{2} + 2

. Find the value of

θ (ψ (- 7))

.

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How to prepare for Quantitative Aptitude for the CAT>Chapter 20 - Functions>Level of Difficulty>Q 59

If

F (a + b) = F (a) . F (b) \div 2

, where

F (b) \neq 0

and

F (a) \neq 0

, then what is the value of

F (12 b) ?

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How to prepare for Quantitative Aptitude for the CAT>Chapter 20 - Functions>Level of Difficulty>Q 60

A function $a = θ (b)$ is said to br reflexive functions?
(i) $\frac{3 b + 5}{4 b - 3}$
(ii) $\frac{3 b + 5}{5 b - 2}$
(iii) $\frac{2 b + 12}{12 b - 2}$

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IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 20 - Functions>Level of Difficulty>Q 67

If

f (x) = \frac{x^{2} + 1}{x - 1}

then

f (f (f (2))) = 2

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 20 - Functions>Level of Difficulty>Q 86

Which of the following curves correctly represents

y = |x - 2|

EASY

CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 20 - Functions>Level of Difficulty>Q 87

Which of the following represents the curves of

y = \log |x| ?