Mathematics

Functions: domain and range Questions

Chapter: Calculus | Total Available: 67 Real Questions

Question 1 of 10 Authentic UPSC NDA Question

What is the range of the function f(x) = l - sin x defined on entire real line?

Step-by-Step Logic & Solution

Question 2 of 10 Authentic UPSC NDA Question

Direction for Questions (67-68): Consider the following for the two (02) items that follow: A function f is such that f(xy) = f(x + y) for all real values of x and y and f(5) = 10

 What if f(20) + f(–20) equal to?

Step-by-Step Logic & Solution

Question 3 of 10 Authentic UPSC NDA Question

Direction for Questions (67-68): Consider the following for the two (02) items that follow: A function f is such that f(xy) = f(x + y) for all real values of x and y and f(5) = 10

What is f(0) equal to?

Step-by-Step Logic & Solution

Explanation: f(0) = f(0 × 5) = f(0 + 5) = f(5) = 10

Question 4 of 10 Authentic UPSC NDA Question

Direction for Questions (65-66): Consider the following for the two (02) items that follow:

 The function f(x) satisfies for all positive real values of x and y, and f(2) = 3

What is f(1) s f(4) equal to?

Step-by-Step Logic & Solution

Question 5 of 10 Authentic UPSC NDA Question

Direction for Questions (65-66): Consider the following for the two (02) items that follow:

The function f(x) satisfiesfor all positive real values of x and y, and f(2) = 3

What is f(16) equal to?

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Question 6 of 10 Authentic UPSC NDA Question

Direction for Questions (61-62): Consider the following for the two (02) items

Let y =What is y equal to?

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Question 7 of 10 Authentic UPSC NDA Question

Direction: Consider the following for the next two items
that follow:What is |U2 (x) – V2 (x)| equal to?

Step-by-Step Logic & Solution

Question 8 of 10 Authentic UPSC NDA Question

Direction: Consider the following for the next two (02)
items that follow:
Let f(t) = ln (t+√1+t2) and g(t) = tan(f(t)).

Consider the following statements:

 I. f(t) is an odd function.

 II. g(t) is an odd function.

Which of the statements given above is/are correct?

Step-by-Step Logic & Solution

Question 9 of 10 Authentic UPSC NDA Question

Direction: Consider the following for the two items that
follow:
Let f(x) = [x]2 – [x2]

.What is f(0.999) + f(1.001) equal to?

Step-by-Step Logic & Solution

Question 10 of 10 Authentic UPSC NDA Question

Which one of the following is g(x)?

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