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Subjects
Class 11MathematicsRelations and FunctionsReal-Valued Functions, Their Domain and RangeMedium
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What is the domain of the real-valued function \(f(x)=\dfrac{\sqrt{3-x}}{x-1}\)?

Answer and explanation

Correct answer: \(( -\infty,1)\cup(1,3]\)

For the square root, \(3-x\geq0\), so \(x\leq3\). Also, the denominator cannot be zero, so \(x=1\) is excluded. In exams, check radical and denominator restrictions separately.

Related tags

Real Valued FunctionsDomain Of FunctionsSquare Root FunctionRational FunctionClass 11 MathematicsTheir Domain And RangeReal Valued Functions Their Domain And RangeRelations And Functions
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10 more MCQs
  1. 1If A = {1,2,3} and R = {(1,2),(2,3)}, which element is in the domain of R but not in its range?
  2. 2If R={(2,5),(4,7),(6,9)}, what is the range of R?
  3. 3If A={1,2,3,4} and R={(a,b): a,b∈A, a+2=b}, what is the domain of R?
  4. 4What is the range of the relation \(R=\{(x,y): y=x^2,\ x\in\{-2,-1,0,1,2\}\}\)?
  5. 5If \(f:A\to B\) is a function, what is \(A\) called?
  6. 6What is the range of the function f = {(1,5), (2,5), (3,6)}?
  7. 7What is the domain of the function \(f=\{(2,4),(3,9),(4,16)\}\)?
  8. 8If \(f(x)=x+2\) and its domain is \(\{1,2,3\}\), what is the value of \(f(2)\)?
  9. 9If \(f(x)=x-1\) and \(A=\{2,3,4\}\), what is \(f(A)\)?
  10. 10If \(A=\{1,4,9\}\) and the function \(f(x)=\sqrt{x}\), what is \(f(A)\)?
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