Class 11 Exam  >  Class 11 Questions  >  What is the real function and real valued fun... Start Learning for Free
What is the real function and real valued function?
Verified Answer
What is the real function and real valued function?
Real-valued function
In mathematics, a real-valued function is a function whose values are real numbers. In other words, it is a function that assigns a real number to each member of its domain.
Many important function spaces are defined to consist of real-valued functions.
Real Function
A function whose range is in the real numbers is said to be a real function, also called a real-valued function.
This question is part of UPSC exam. View all Class 11 courses
Most Upvoted Answer
What is the real function and real valued function?
Understanding Real Functions
Real functions are mathematical expressions that relate inputs from the real number system to outputs also within the real number system.
Key Characteristics of Real Functions:
- Real functions take real numbers as input.
- Each input is associated with exactly one output.
- They can be represented as f(x), where x is a real number.
- Examples include linear functions (f(x) = mx + b), quadratic functions (f(x) = ax^2 + bx + c), and trigonometric functions (f(x) = sin(x)).
Understanding Real-Valued Functions
Real-valued functions are a subset of real functions where the outputs are specifically real numbers. This means that for every input in the function’s domain, the output must also be a real number.
Key Characteristics of Real-Valued Functions:
- They produce real number outputs regardless of the input.
- The domain and range of these functions are typically subsets of the real numbers.
- Examples include f(x) = x^2, where for any real input x, the output is also a real number.
Differences Between Real Functions and Real-Valued Functions:
- All real-valued functions are real functions, but not all real functions are real-valued.
- Real functions may include complex numbers or other types, while real-valued functions strictly produce real outputs.
Conclusion
In summary, real functions encompass a broader category that includes any relationship between real numbers, whereas real-valued functions are specifically those that yield real number outputs. Understanding these distinctions is crucial in mathematical analysis and applications.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
Explore Courses for Class 11 exam

Top Courses for Class 11

What is the real function and real valued function?
Question Description
What is the real function and real valued function? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about What is the real function and real valued function? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the real function and real valued function?.
Solutions for What is the real function and real valued function? in English & in Hindi are available as part of our courses for Class 11. Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of What is the real function and real valued function? defined & explained in the simplest way possible. Besides giving the explanation of What is the real function and real valued function?, a detailed solution for What is the real function and real valued function? has been provided alongside types of What is the real function and real valued function? theory, EduRev gives you an ample number of questions to practice What is the real function and real valued function? tests, examples and also practice Class 11 tests.
Explore Courses for Class 11 exam

Top Courses for Class 11

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev