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 (f(x)=\lfloor x+2\rfloor) and (x\in[-1,3)), what is the range of (f)?If (f(x)={2x}) is the fractional part function and (x\in\mathbb{R}), what is the range?If (f(x)=\lceil 3x\rceil) and (x\in(0,1]), what is the range of (f)?What is the range of (f(x)=\frac{1}{2+\sqrt{x^2+1}})?What is the range of \(f(x)=\frac{x}{\sqrt{x^2+9}}\)?What is the range of (f(x)=\frac{x-2}{\sqrt{x^2-4x+8}})?What is the range of (f(x)=\frac{x^2+1}{x})?What is the range of (f(x)=\frac{x^2+9}{3x})?What is the domain of (f(x)=\sqrt{\frac{9-x^2}{x^2-4}})?What is the domain of (f(x)=\sqrt{\frac{x^2-1}{4-x^2}})?What is the domain of (f(x)=\frac{\sqrt{x+3}}{\sqrt{2-x}})?What is the range of (f(x)=\frac{\sqrt{x+3}}{\sqrt{2-x}})?What is the domain of (f(x)=\sqrt{1-\frac{1}{x^2}})?What is the range of (f(x)=\sqrt{1-\frac{1}{x^2}})?Which of the following functions has domain all real numbers and range \((0,1]\)?What is the domain of (f(x)=\sqrt{\log_{\frac{1}{4}}(9-x)})?What is the range of (f(x)=\frac{2}{3+\sqrt{x^2+4}})?If the function (f(x)=x^3) is given, what is the value of (f(-2))?What is the range of the function \(f(x)=x^2\) defined over the real numbers?What is the range of the function \(f(x)=x^3\)?