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Class 11MathematicsRelations and FunctionsReal-Valued Functions, Their Domain and RangeExpert
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What is the range of the function \(f(x)=\sqrt{6x-x^2-5}\)?

Answer and explanation

Correct answer: [0,2]

The radicand can be rewritten as \(6x-x^2-5=4-(x-3)^2\). For the function to be real, \((x-3)^2\leq 4\), giving the domain \([1,5]\). The radicand varies from 0 to 4, so taking its square root gives \(f(x)\in[0,2]\). Option C is the range of the radicand, not of the function. Exam tip: for a square-root function, first find the range of the expression under the root and then apply the square root.

Related tags

Real-Valued-FunctionsRangeDomainRadical-FunctionsQuadratic-FunctionsReal Valued FunctionsTheir 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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