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 (f(x)=\frac{1}{x^2-6x+10})?If \(f(x)=\sqrt{x}+\sqrt{6-x}\), what is its domain as a real-valued function?What is the maximum value of (f(x)=\sqrt{x}+\sqrt{6-x})?If (f(x)=x^2) and the domain is ([-5,-2]), what is the range?What is the range of (f(x)=\frac{x}{x^2+1}) where (x\in\mathbb{R})?If (f(x)=\frac{x^2+2x+5}{x^2+2x+2}), what is the range of (f)?What is the range of (f(x)=\frac{1}{|x|+1})?If (f(x)=\sqrt{|x|-3}), what is the domain?What is the range of (f(x)=|x-1|-|x+2|)?If (f(x)=\frac{1}{\sqrt{x-2}}+\sqrt{8-x}), what is the domain?Which ordered pair correctly classifies the domain and range of the real-valued function \(f(x)=\dfrac{x^2}{1+x^2}\)? In each ordered pair, the first set represents the domain and the second set represents the range.If (f(x)=\frac{x^2-1}{x^2+1}), what is the range of (f)?What is the domain of the real-valued function \(f(x)=\sqrt{x-1}+\sqrt{x-4}\)?If (f(x)=\sqrt{x-1}+\sqrt{x-4}), what is the range of (f)?What is the maximum value of (f(x)=\frac{1}{x^2+2x+5})?What is the domain of the function 8f(x)=\sqrt{2-|x-1|}9?If (f(x)=\sqrt{2-|x-1|}), what is the range of (f)?What is the domain of (f(x)=\frac{1}{\sqrt{|x+2|-5}})?If (f(x)=\frac{4x-1}{2x+5}), what is the range of (f)?If (f(x)=\frac{\sqrt{(x-2)(7-x)}}{x^2-9}), what is the domain of (f)?