English
Hindi

Question

Download Solution PDF

Let f : R → R be defined by f(x) = sin x, and g : R → R be defined by g(x) = x2. Find (f o g)(x).

  1. x2 sin x
  2. sin2 x
  3. sin x2
  4. 2x sin x

Answer (Detailed Solution Below)

Option 3 : sin x2
Free Tests
View all Free tests >
Free
Army Havildar SAC - Quick Quiz
5 Qs. 10 Marks 6 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

  • For two functions f(x) and g(x), (f o g)(x) is defined as f[g(x)].

 

Calculation:

f(x) = sin x and g(x) = x2.

∴ (f o g)(x) = f[g(x)] = sin [g(x)] = sin (x2) = sin x2.

Download Solution PDF
Latest Army Havildar SAC Updates

Last updated on Jun 11, 2025

-> The Indian Army has released the official notification for the post of Indian Army Havildar SAC (Surveyor Automated Cartographer).

-> Interested candidates had applied online from 13th March to 25th April 2025.

-> Candidates within the age of 25 years having specific education qualifications are eligible to apply for the exam.

-> The candidates must go through the Indian Army Havildar SAC Eligibility Criteria to know about the required qualification in detail. 

Exams Tests Super Practice

More Composition of Functions Questions

Q1.Which one of the following is g(x)? 
Q2.Which one of the following is f(x)? 
Q3.f f(x) = 9x - 8√x such that g(x) = f(x) - 1, then which one of the following is correct?
Q4.If f(x) = 4x + 1 and g(x) = kx + 2 such that f o g(x) = g o f(x), then what is the value of k?  
Q5.Let f : R → R be defined as f(x) = 2x - 1 and g:R – {1} → R be defined as g(x) = (x - 1/2)/(x - 1). Then the composition function f(g(x)) is:
Q6.If g(x) = x2 + x – 1 and (gof)(x) = 4x2 – 10x + 5, then \(f\left(\frac{5}{4}\right) \) is equal to
Q7.Let ƒ(x) = x5 + 2ex/4 for all x ∈ R. Consider a function g(x) such that (gof) (x) = x for all x ∈ R. Then the value of 8g'(2) is :
Q8.If f(x) = x2 + 2 and g(x) = 2x - 3 are real function, then (fog) (x) is:
Q9.Let f ∶ R → R be the function defined by f(x) = \(\rm\frac{2x-1}{2}\) and g ∶ Q → R be another function defined by g(x) = x + 2. Then (g o f) \(\frac{3}{2}\) is
Q10.Let f ∶ [0, 1] → [0, 1] be defined by f(x) = \(\left\{\begin{array}{c}x, \text { if } x \text { is rational } \\ 1−x, \text { if } x \text { is irrational }\end{array}\right.\) Then (f o f) x is

More Relations and Functions Questions

Q1.Which one of the following is g(x)? 
Q2.Which one of the following is f(x)? 
Q3.Let f(x) f(y) = f(xy) for all real x, y. If f(2) = 4, then what is the value of f(1/2)?
Q4.f f(x) = 9x - 8√x such that g(x) = f(x) - 1, then which one of the following is correct?
Q5.lf f(x) = [x]2 - 30[x] + 221 = 0, where [x] is the greatest integer function, then what is the sum of all integer solutions? 
Q6.If f(2x) = 4x2 + 1, then for how many real values of x will f(2x) be the GM of f(x) and f(4x)?  
Q7.If f(x) = 4x + 1 and g(x) = kx + 2 such that f o g(x) = g o f(x), then what is the value of k?  
Q8.Let z = [y] and y = [x] - x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z? 
Q9.If A and B are two non-empty sets having 10 elements in common, then how many elements do A x B and B x A have in common?
Q10.Let P and Q be two non-void relations on a set A. Which of the following statements are correct? I. P and Q are reflexive ⇒ P ∩ Q is reflexive. II. P and Q are symmetric ⇒ P ∪ Q is symmetric. III. P and Q are transitive ⇒ P ∩ Q is transitive. Select the answer using the code given below.
Suggested Test Series
View All >
Army Havildar SAC Mock Test Series 2025
121 Total Tests with 3 Free Tests
Start Free Test
NCERT XI-XII Math Foundation Pack Mock Test
117 Total Tests with   5 Free Tests
Start Free Test

Army Havildar SAC Important Links

Eligibility CriteriaSalary and Job ProfileAdmit CardSyllabus and Exam PatternAnswer KeyCut Off

More Mathematics Questions

Q1.If cosec θ + cot θ = p, then \(\rm\frac{p^2-1}{p^2+1}\) equal:
Q2.In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?
Q3.Three perfect dice D1, D2 and D3 and are rolled. Let x, represent the numbers on D1, D2 and D3 respectively. What is the number of possible outcomes such that x < y < z?
Q4.Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?
Q5.The occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?
Q6.Two perfect dice are thrown. What C is the probability that the sum of the numbers on the faces is neither 9 nor 10?
Q7.Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?
Q8.A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?  
Q9.The mean of the series x1, x2...xn is x̅ If xn is replaced by k, then what is the new mean?
Q10.Let \(\rm \Sigma_{i=1}^9x_i^2=885\) If M is the mean and σ is the standard deviation of  x1, x2, x3.....x9 then what is the value of M2 + σ2?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti rules teen patti master golden india teen patti casino apk teen patti all games