Test: Functions- 4


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


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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 ____________

Solution:

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

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)

Solution:

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.

QUESTION: 3

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

Solution:

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

QUESTION: 4

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

Solution:

(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.

QUESTION: 5

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

Solution:

(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)).

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

Solution:

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

QUESTION: 7

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

Solution:

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.

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)]

Solution:

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

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)]

Solution:

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

QUESTION: 10

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

Solution:

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.

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}].

Solution:

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

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].

Solution:

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

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

Solution:

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

QUESTION: 14

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

Solution:

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

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

Solution:

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.

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