This EduRev document offers 10 Multiple Choice Questions (MCQs) from the topic Functions (Level - 2). These questions are of Level - 2 difficulty and will assist you in the preparation of CAT & other MBA exams. You can practice/attempt these CAT Multiple Choice Questions (MCQs) and check the explanations for a better understanding of the topic.
Question for Practice Questions Level 2: Functions - 1
Try yourself:If f(x) = then f (2x) is:
Explanation
We have f(x) =
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Question for Practice Questions Level 2: Functions - 1
Try yourself: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?
Question for Practice Questions Level 2: Functions - 1
Try yourself:The graph of function f(x) = 2x is shown below.
Which of the following graphs correctly represents the function g(x) = 2x - 2?
Explanation
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.
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Question for Practice Questions Level 2: Functions - 1
Try yourself:A function is defined as y = f(x) = 2x + 3. Find the co-ordinates of a point such that x = f(y).
Explanation
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.
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Question for Practice Questions Level 2: Functions - 1
Try yourself:Find out whether the functions are odd or even.
(i) y = 2-x2
(ii) y = 2x - x4
Explanation
(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
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Question for Practice Questions Level 2: Functions - 1
Try yourself:If f(x) = x3 - x2 - x + 1 and g(x) = x2 - 2x + 1, which of the following relations is true?
Question for Practice Questions Level 2: Functions - 1
Try yourself:If f(x) = xx, find the value of [f (- x)]2 in terms of f(x).
Explanation
[f(-x)]2 = [-x-x]2 = (-x)-2x = (x)-2x =
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Question for Practice Questions Level 2: Functions - 1
Try yourself:If f(x) is an odd function, then |f(x)| is
Explanation
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.
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Question for Practice Questions Level 2: Functions - 1
Try yourself:The graph of f(x) and its transformation is given below. What is the expression for its transformation in terms of f(x)?
Explanation
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).
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Question for Practice Questions Level 2: Functions - 1
Try yourself:If f(x) = 2x - 6, then f(f(f(-2))) is equal to