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# Test: Functions- 4

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## 15 Questions MCQ Test Quantitative Aptitude (Quant) | Test: Functions- 4

Test: Functions- 4 for CAT 2022 is part of Quantitative Aptitude (Quant) preparation. The Test: Functions- 4 questions and answers have been prepared according to the CAT exam syllabus.The Test: Functions- 4 MCQs are made for CAT 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Functions- 4 below.
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Test: Functions- 4 - Question 1

### Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = 3x + 4. Then the composition of f and g is ____________

Detailed Solution for Test: Functions- 4 - Question 1

The composition of f and g is given by f(g(x)) which is equal to 2(3x + 4) + 1.

Test: Functions- 4 - Question 2

### A certain function always obeys the rule: If f (x.y) = f(x). f(y) where x and y are positive realnumbers. A certain Mr. Mogambo found that the value of f (128) = 4, then find the value of thevariable M = f (0.5). f (1). f (2). f (4). f (8). f (16). f (32). f (64). f (128). f (256)

Detailed Solution for Test: Functions- 4 - Question 2

Since f (128) = 4, we can see that the product of f (256). f (0.5) = f (256 × 0.5) = f (128) = 4.
Similarly, the products f (1). f (128) = f (2). f (64)
= f (4). f (32) = f (8). f (16) = 4.
Thus, M = 4 × 4 × 4 × 4 × 4 = 1024.
Option (d) is the correct answer.

Test: Functions- 4 - Question 3

### If f(t) = 2t, then f(0), f(1), f(2) are in

Detailed Solution for Test: Functions- 4 - Question 3

f(0) = 1, f(1) = 2 and f(2) = 4
Hence, they are in G.P.

Test: Functions- 4 - Question 4

The graph of y = (x + 3)3 + 1 is the graph of y = x3 shifted

Detailed Solution for Test: Functions- 4 - Question 4

(x + 3)3 would be shifted 3 units to the left and hence (x + 3)3 + 1 would shift 3 units to the left
and 1 unit up. Option (c) is correct.

Test: Functions- 4 - Question 5

If f(x) = x2 and g(x) = logex, then f(x) + g(x) will be

Detailed Solution for Test: Functions- 4 - Question 5

(x2 + loge x) would be neither odd nor even since it obeys neither of the rules for even function
(f(x) = f(–x)) nor for odd functions (f(x) = –f(–x)).

Test: Functions- 4 - Question 6

f(x) is any function and f–1(x) is known as inverse of f(x), then f–1(x) of f(x) = ex is

Detailed Solution for Test: Functions- 4 - Question 6

y = ex
fi loge y = x.
fi f –1(x) = loge x.

Test: Functions- 4 - Question 7

Which of the following functions will have a minimum value at x = –3?

Detailed Solution for Test: Functions- 4 - Question 7

If you differentiate each function with respect to x, and equate it to 0 you would see that for none
of the three options will get you a value of x = –3 as its solution. Thus, option (d) viz. None of
these is correct.

Test: Functions- 4 - Question 8

Define the following functions:

f(x, y, z) = xy + yz + zx

g(x, y, z) = x2y + y2z + z2x and

h(x, y, z) = 3 xyz

Q.

Find the value of the following expressions:37. h[f(2, 3, 1), g(3, 4, 2), h(1/3, 1/3, 3)]

Detailed Solution for Test: Functions- 4 - Question 8

The given function would become h[ 11, 80, 1] = 2640.

Test: Functions- 4 - Question 9

Define the following functions:
f(x, y, z) = xy + yz + zx
g(x, y, z) = x2y + y2z + z2x and
h(x, y, z) = 3 xyz
Find the value of the following expressions:

Q.

f[ f (1, 1, 1), g(1, 1, 1), h(1, 1, 1)]

Detailed Solution for Test: Functions- 4 - Question 9

The given function would become f[3, 3, 3] = 27.

Test: Functions- 4 - Question 10

If f(x) = 1/ g(x), then which of the following is correct?

Detailed Solution for Test: Functions- 4 - Question 10

The number of g’s and f’s should be equal on the LHS and RHS since both these functions are
essentially inverse of each other.
Option (c) is correct.

Test: Functions- 4 - Question 11

If R(a/b) = Remainder when a is divided by b;
Q(a/b) = Quotient obtained when a is divided by b;
SQ(a) = Smallest integer just bigger than square root of a.

Q.

If a = 12, b = 5, then find the value of SQ[R {(a + b)/b}].

Detailed Solution for Test: Functions- 4 - Question 11

SQ [R[(a + b)/b]] = SQ [R[17/5]] fi SQ  = 2.

Test: Functions- 4 - Question 12

If R(a/b) = Remainder when a is divided by b;
Q(a/b) = Quotient obtained when a is divided by b;
SQ(a) = Smallest integer just bigger than square root of a.

Q.

If a =18, b = 2 and c = 7, then find the value of Q [{SQ(ab) + R(a/c)}/b].

Detailed Solution for Test: Functions- 4 - Question 12

Q [[SA (36) + R (18/7)]/2] = Q [(7 + 4)/2] = Q [11/2] = 5.

Test: Functions- 4 - Question 13

Read the following passage and try to answer questions based on
them.
[x] = Greatest integer less than or equal to x
{x} = Smallest integer greater than or equal to x.

Q.

If x is not an integer, then ({x} + [x]) is

Detailed Solution for Test: Functions- 4 - Question 13

[x] + {x} will always be odd as the values are consecutive integers.

Test: Functions- 4 - Question 14

If f(t) = t2 + 2 and g(t) = (1/t) + 2, then for t = 2, f [g(t)] – g[f(t)] = ?

Detailed Solution for Test: Functions- 4 - Question 14

f(g(t)) – g(f(t)) = f(2.5) – g(6) = 8.25 – 2.166 = 6.0833.

Test: Functions- 4 - Question 15

Let F(x) be a function such that F(x) F(x + 1) = – F(x – 1)F(x–2)F(x–3)F(x–4) for all x ≥ 0.Given the values of If F (83) = 81 and F(77) = 9, then the value of F(81) equals to

Detailed Solution for Test: Functions- 4 - Question 15

When the value of x = 81 and 82 is substituted in the given expression, we get,
F (81) F (82) = – F (80) F (79) F(78) F(77)
F (82) F (83) = – F (81) F (80) F(79) F(78)
On dividing (i) by (a), we get Option (a) is the correct answer.

## Quantitative Aptitude (Quant)

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## Quantitative Aptitude (Quant)

163 videos|152 docs|131 tests

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