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Test Level 2: Functions - 1 - CAT MCQ


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10 Questions MCQ Test Level-wise Tests for CAT - Test Level 2: Functions - 1

Test Level 2: Functions - 1 for CAT 2024 is part of Level-wise Tests for CAT preparation. The Test Level 2: Functions - 1 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 2: Functions - 1 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 2: Functions - 1 below.
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Test Level 2: Functions - 1 - Question 1

If f(x) = then f (2x) is:

Detailed Solution for Test Level 2: Functions - 1 - Question 1

We have f(x) = 

Test Level 2: Functions - 1 - Question 2

Directions: If x and y are real numbers, the functions are defined as f(x, y) = |x2 + y2| and F(x, y) = –f(x, y) = –G(x, y).
Now with the help of this information, answer the following question.
Which of the following will be necessarily true?

Detailed Solution for Test Level 2: Functions - 1 - Question 2

Since f(x, y) = |x2 + y2| and F(x, y) = –f(x, y);
F(x, y) = –|x2 + y2|
Again, G(x, y) = –F(x, y)
So, G(x, y) = |x2 + y2|
Hence, G(x, y) = f(x, y)

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Test Level 2: Functions - 1 - Question 3

The graph of function f(x) = 2x is shown below.

Which of the following graphs correctly represents the function g(x) = 2x - 2?

Detailed Solution for Test Level 2: Functions - 1 - Question 3

As x is replaced by (x - 2),
The graph function of g(x) = 2x - 2 is obtained by shifting the graph of function f(x) = 2x two units towards right.

Test Level 2: Functions - 1 - Question 4

A function is defined as y = f(x) = 2x + 3. Find the co-ordinates of a point such that x = f(y).

Detailed Solution for Test Level 2: Functions - 1 - Question 4

Let ( x1, y1) be the required point.
Therefore, y1 = f(x1) = 2x1 + 3.....(i)
But x1 = f(y1) = 2y1 + 3.....(ii)
From (i) and (ii), we get
y1 = 2x1 + 3
y1 = 
Therefore, x1 = -3 and y1 = -3.

Test Level 2: Functions - 1 - Question 5

Find out whether the functions are odd or even.
(i) y = 2-x2
(ii) y = 2x - x4

Detailed Solution for Test Level 2: Functions - 1 - Question 5

(i) f(x) = y = 2-x2 ; f(- x) = -2x2  = f(x) ; Therefore function is an even function
(ii) f(x) = y = 2x - x4; f(- x) = 2x - x4: Therefore function is neither even nor odd

Test Level 2: Functions - 1 - Question 6

If f(x) = x3 - x2 - x + 1 and g(x) = x2 - 2x + 1, which of the following relations is true?

Detailed Solution for Test Level 2: Functions - 1 - Question 6

f(x) = x3 - x2 - x + 1 = (x + 1) (x - 1)2 and g(x) = x2 - 2x + 1 = (x - 1)2.
Hence, f(x) = (x + 1) . g(x)

Test Level 2: Functions - 1 - Question 7

If f(x) = xx, find the value of [f (- x)]2 in terms of f(x).

Detailed Solution for Test Level 2: Functions - 1 - Question 7

[f(-x)]2 = [-x-x]2 = (-x)-2x = (x)-2x

Test Level 2: Functions - 1 - Question 8

If f(x) is an odd function, then |f(x)| is

Detailed Solution for Test Level 2: Functions - 1 - Question 8

If f(x) is an odd function, then |f(x)| will become an even function.
An odd function is defined by f(-x) = -f(x)
If the modulus of the function will be taken, it will become positive.
Also the graph in the negative y-axis will shift to the positive y-axis.
|f(-x)| = |-f(x)| = f(x), which is the definition of even function.

Test Level 2: Functions - 1 - Question 9

The graph of f(x) and its transformation is given below. What is the expression for its transformation in terms of f(x)?

Detailed Solution for Test Level 2: Functions - 1 - Question 9

Here, f(x) is shifted 3 steps to the left. From the graph, you can see that f(0) = f(3), f(1) = f(4).
This is a horizontal translation of graph, which is obtained when input is increased by 3.
Hence, the only option that satisfies is f(x + 3).

Test Level 2: Functions - 1 - Question 10

If f(x) = 2x - 6, then f(f(f(-2))) is equal to

Detailed Solution for Test Level 2: Functions - 1 - Question 10

f(x) = 2x - 6
f(-2) = 2 × (-2) - 6 = -10
f(f(-2)) = f(-10) = 2 × (-10) - 6 = -26
f(f(f(-2))) = f(f(-10)) = f(-26)
f(-26) = 2 × (-26) - 6 = -58
f(f(f(-2))) = -58

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