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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 \(f:\mathbb{R}\to\mathbb{R}\) has range \([-2,\infty)\) and \(f(x)=(x-a)^2+b\), which of the following pairs \((a,b)\) is possible?If the function \\(f:\mathbb{R}\to\mathbb{R}\\) is defined by \\(f(x)=2x^2-8x+11\\), what is the range of \\(f\\)?If f: {0,1,2,3,4,5} → {0,1,2,3,4,5} is defined such that f(x) is the remainder when 4x is divided by 6, what is the range of f?If the function \(f:\{1,2,3,4,5,6,7,8,9\}\to\{0,1\}\) is defined by \(f(n)=1\) when \(n\) is divisible by \(3\), and \(f(n)=0\) otherwise, what is \(f^{-1}(\{1\})\)?If (f:mathbb{R} omathbb{R}) has range ([5,infty)) and (f(x)=a(x-2)^2+b), where (a>0), which of the following pairs is possible?If (f(x)=x+3) is a real valued function, what is its domain?What is the range of (f(x)=x^2) when the domain is (\mathbb{R})?What is the real domain of the function \(f(x)=\sqrt{x}\)?What is the domain of (f(x)=\frac{1}{x})?What is the range of (f(x)=5)?If f(x)=2x-1, what is the value of f(3)?What is the real domain of (f(x)=\sqrt{x-2})?What is the range of the function \(f(x)=x^2+1\) when \(x\in\mathbb{R}\)?What is the range of the function 8f(x)=|x|9?What is the domain of the function \(f(x)=\frac{1}{x-4}\)?If \(f:\mathbb{R}\to\mathbb{R}\) and \(f(x)=3x\), what is the value of \(f(-2)\)?What is the real domain of the function \(f(x)=\sqrt{5-x}\)?What is the range of the function \(f(x)=2x^2\) when \(x\in\mathbb{R}\)?What are the domain and range of (f(x)=x^3)?If the function \(f(x)=x+1\) has the domain \(A=\{1,2,3\}\), what is its range?