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Class 11MathematicsRelations and FunctionsReal-Valued Functions, Their Domain and RangeMedium
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What is the range of the function \\(f(x)=2\\sqrt{x+1}-5\\)?

Answer and explanation

Correct answer: \\([-5,\\infty)\\)

For the square root to be defined, \\(x+1\\ge 0\\), and \\(\\sqrt{x+1}\\ge 0\\). Thus, \\(2\\sqrt{x+1}\\ge 0\\), so \\(f(x)=2\\sqrt{x+1}-5\\ge -5\\). At \\(x=-1\\), the function equals \\(-5\\), and as \\(x\\) increases, the function values grow without bound. Therefore, the range is \\([-5,\\infty)\\). Option C ignores the downward shift by \\(-5\\). Exam tip: Find the minimum value of the square-root part first, then account for any vertical translation.

Related tags

Standard-FunctionsSquare-Root-FunctionsRangeGraph-TransformationsReal Valued FunctionsTheir Domain And RangeReal Valued Functions Their Domain And RangeRelations And FunctionsMathematics
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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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