This EduRev document offers 10 Multiple Choice Questions (MCQs) from the topic Functions (Level - 1). These questions are of Level - 1 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 1: Functions - 1
Try yourself:If f(x) = y and g(x) = y2 + 1, find g(f(x)).
Explanation
f(x) = y
g(f(x)) = g(y) = y2 + 1
The dependent variable always remains constant, irrespective of the independent variable.
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Question for Practice Questions Level 1: Functions - 1
Try yourself:If , then
Explanation
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Question for Practice Questions Level 1: Functions - 1
Try yourself:The graph of the function y = 5x6 + 3x4 - x2 + 8
Explanation
If y = f (x), f (x) = f (- x).
So the y values are the same for +ve and -ve values of x, and the graph is symmetric about the Y-axis.
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Question for Practice Questions Level 1: Functions - 1
Try yourself:If f(x, y) = 3x2 - 2xy - y2 + 4, find f(1, -1).
Explanation
Substituting x = 1 and y = -1 in f(x, y), we get
f(1, -1) = 3 (1)2 - 2 × (1) (-1) - (-1)2 + 4 = 8
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Question for Practice Questions Level 1: Functions - 1
Try yourself:The given graph is
Explanation
Graph is symmetric about Y - axis;
y = f(x) = I x I
f(-x) = I- x I = I x I
f(-x) = f(x)
therefore it is an even function.
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Question for Practice Questions Level 1: Functions - 1
Try yourself:A function is defined as f(x) = + 1 + x + 2x2 + 3x3 + 4x4 + 5x5. If f(2) = 260.78, what is the value of f?
Explanation
f(x) = + 1 + x + 2x2 + 3x3 + 4x4 + 5x5
f(1/x) = 5x5 + 4x4 + 3x3 + 2x2 + x + 1 +
f(x) = f(1/x)
Therefore, f(1/2) = f(2) = 260.78.
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Question for Practice Questions Level 1: Functions - 1
Try yourself:Find the range of the function f(x) =
Explanation
f(x) =
Let, y = f(x)
⇒ y2 = x - 3
⇒ x = y2 + 3
f-1(x) = x2 + 3
Domain of f-1(x) = R ....(i)
f(x) > 0 ......(ii)
Hence from (i) and (ii)
Range of f(x) = (0, ∞)
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Question for Practice Questions Level 1: Functions - 1
Try yourself:f : → R and g : R → R are defined as f (x) = x2 and g (x) = x + 3, x ∈ R, then (fog) (x) = ?
Explanation
f(x) = x2, g(x) = x + 3
(fog) (x) = f(x + 3) = (x + 3)2 = x2 + 6x + 9.
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Question for Practice Questions Level 1: Functions - 1
Try yourself:Let a function be fn+1(x) = fn (x) + 3 . If f2(2) = 4, find the value of f6(2).
Explanation
We have, fn+1(x) = fn (x) + 3
So, f3(2) = f2(2) + 3 = 7
f4(2) = f3(2) + 3 = 10
f5(2) = f4(2) + 3 = 13
f6(2) = f5(2) + 3 = 16
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Question for Practice Questions Level 1: Functions - 1
Try yourself:Let A = {a, b, c}. Then, the range of the relation R = {(a, b), (a, c), (b, c)} defined on A is
Explanation
Range of R = {y ∈ A : (x, y) ∈ R for some x ∈ A} = {b, c}
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