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Mathematics

Real-Valued Functions, Their Domain and Range

वास्तविक मान वाले फलन, उनके प्रांत और परास

In Class 11 Mathematics, under Relations and Functions, students study real-valued functions and identify their domain, codomain, range and image. They learn to represent functions through ordered pairs, rules and sets, determine allowable input values, and find the corresponding output values. The topic also develops understanding of function values and ranges for simple algebraic functions.

Practice questions

What is the range of the relation \(R=\{(x,y): y=x^2,\ x\in\{-2,-1,0,1,2\}\}\)?If \(f:A\to B\) is a function, what is \(A\) called?What is the domain of the function \(f=\{(2,4),(3,9),(4,16)\}\)?If \(f(x)=x+2\) and its domain is \(\{1,2,3\}\), what is the value of \(f(2)\)?If \(f(x)=x-1\) and \(A=\{2,3,4\}\), what is \(f(A)\)?If \(A=\{1,4,9\}\) and the function \(f(x)=\sqrt{x}\), what is \(f(A)\)?Which of the following functions has all real numbers as its domain?What is the domain of the function \(f=\{(5,1),(6,1),(7,2)\}\)?If A is a non-empty set and \(f(x)=10\) for every x \(\in A\), what is the range of \(f\)?If A = {2, 4, 6} and the function f(x) = x − 2, what is f(A)?If \(f(x)=x^2\) and \(f(a)=16\), what is the positive value of \(a\)?If \(A=\{1,2\}\), \(B=\{3,4\}\), and \(f=\{(1,3),(2,3)\}\), what is the range of \(f\)?If the function \(f(x)=x+1\) has domain \(\{0,2,4\}\), what is its range?Which of the following functions has the set of all real numbers as its domain?What is the domain of the function f = {(3, 10), (5, 12), (7, 14)}?What is the range of the function \(g=\{(1,4),(2,6),(3,8),(4,10)\}\)?If f(x)=x−4 and the domain of the function is A={4,5,9}, what is the value of f(A)?If \(f:A\to B\) is a function, which statement correctly describes the relationship between its range and codomain?If \(f(x)=|x|\) and \(A=\{-2,0,3\}\), what is the image set \(f(A)\)?If \(A=\{1,2,3\}\) and \(B=\{0,1,2\}\), and \(f:A\to B\) is defined by \(f(x)\) being the remainder when \(x\) is divided by 2, what is the range of \(f\)?