Mathematics
Domain and range
परिभाषा-क्षेत्र और परास
In this Class 12 Mathematics topic from the chapter Inverse Trigonometric Functions, students learn to identify the domain—the set of permitted input values—and the range—the resulting output values—of functions and inverse trigonometric functions. The topic explains how restrictions on sine, cosine and tangent functions make inverse functions well-defined, how principal value ranges are selected, and how domains and ranges can be interpreted from formulas, graphs and function relationships.
Practice questions
What is the domain of \(\sec^{-1}x\)?What is the domain of \(cosec^{-1}x\)?What is the domain of \(\sin^{-1}x\)?Which is the domain of \(\cos^{-1}x\)?What is the domain of tan⁻¹x?Which statement is correct about \(\cos^{-1}\left(-2\right)\)?Which statement is correct for \(\sin^{-1}\left(\frac{7}{6}\right)\)?Which option is correct for \(\cos^{-1}\left(\frac{11}{10}\right)\)?Which statement is correct for \(\sec^{-1}\left(\frac{3}{2}\right)\)?Which statement is correct for \(cosec^{-1}\left(-\frac{5}{4}\right)\)?Which of the following expressions is defined?For which value of x is the function \(\csc^{-1}x\) not defined?For which (x) is \(\sin^{-1}(2x)\) defined as a real number?If \(y=\sin^{-1}x\), what is the correct domain of \(x\)?Under which condition is \(\sin(\sin^{-1}x)\) equal to \(x\)?For \(\sin^{-1}(2x)\) to be defined, in which interval must \(x\) lie?Which is the correct domain interval of \(\cos^{-1}(3x-1)\)?What is the domain of \(x\) for \(sin^{-1}(x^2-1)\)?What is the domain of \(\tan^{-1}(x^2+1)\)?On which set is \(cosec^{-1}x\) defined?