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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

If A = {1, 2, 3}, B = {1, 3, 5, 7}, and f(x) = 2x − 1, what is the range of f?If \(f=\{(2,1),(4,2),(6,3),(8,4)\}\), what is the domain of \(f\)?If \(f:\{1,2,3,4\}\to\{1,2,3,4\}\) and \(f(x)=5-x\), what is the range of \(f\)?If \(f=\{(x,y): y=\frac{x+1}{2},\ x\in\{1,3,5,7\}\}\), what is the range of \(f\)?If \(f:A\to B\) is a function where \(A=\{1,2,3\}\), \(B=\{a,b,c,d\}\), and \(f=\{(1,a),(2,b),(3,b)\}\), what is the range of \(f\)?If \(f:A\to B\) is a function and \(f=\{(a,1),(b,2),(c,1),(d,3)\}\), what is \(A\)?If \(f:\{1,2,3,4\}\to\{0,1\}\) is defined such that \(f(x)=0\) when \(x\) is even and \(f(x)=1\) when \(x\) is odd, what is the range of \(f\)?Which of the following correctly describes the domain and range of the real-valued function \(f(x)=\frac{x^2+1}{x^2-1}\)?Let \(A=\{1,2,3,4\}\) and define \(f:A\to\mathbb{Z}\) by \(f(x)=(-1)^x\). What is the range of \(f\)?If \(f:\{0,1,2,3\}\to\{0,1,2,3\}\) is defined such that \(f(x)\) is the remainder obtained when \(x\) is divided by 3, which of the following statements is correct?If \(A=\{a,b,c,d\}\) and \(B=\{1,2,3\}\), how many functions from \(A\) to \(B\) have range exactly \(\{1,2\}\)?If \(f:\{0,1,2,3\}\to\{0,1,2,3\}\) is defined by \(f(x)\) as the remainder obtained when \(2x\) is divided by 4, what is the range of \(f\)?If \(f:\{1,2,3,4,5,6\}\to\{0,1\}\) is defined by \(f(n)=0\) when \(n\) is divisible by \(3\), and \(f(n)=1\) otherwise, what is \(f^{-1}(\{0\})\)?If \(f:\mathbb{R}\to\mathbb{R}\) is defined by \(f(x)=\begin{cases}x+2,&x<0\\x^2,&x>0\end{cases}\), why is it not a function from \(\mathbb{R}\) to \(\mathbb{R}\)?If the function \(f:\{1,2,3,4\}\to\{1,2,3\}\) is defined by \(f(x)=\min(x,3)\), what is its range?If \(f:\{1,2,3,4\}\to\{1,2,3,4\}\) is defined by \(f(x)=x\) when \(x\) is odd and by \(f(x)=5-x\) when \(x\) is even, what is its range?If \(f:\{0,1,2,3,4\}\to\{0,1,2,3,4\}\) is defined by the remainder obtained when \(3x\) is divided by \(5\), what is the range of \(f\)?If the function \(f:\{1,2,3,4,5,6,7,8\}\to\{0,1\}\) is defined by \(f(n)=1\) when \(n\) is divisible by \(4\), and \(f(n)=0\) otherwise, what is \(f^{-1}(\{1\})\)?If \(f:\{1,2,3,4,5\}\to\{1,2,3\}\) is defined by \(f(x)=\max(1,4-x)\), what is its range?For the function defined by \(f(x)=\frac{1}{|x+1|-3}\), what is its largest possible real domain?