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Subjects
Class 11MathematicsRelations and FunctionsReal-Valued Functions, Their Domain and RangeMedium
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What is the value of the function \(f(x)=|x|-|x-2|\) at \(x=3\)?

Answer and explanation

Correct answer: 2

Substituting \(x=3\), we get \(f(3)=|3|-|3-2|=3-1=2\). Therefore, the correct answer is 2. The distractor 4 results from adding \(|1|\) instead of subtracting it. Exam tip: first substitute the given value into every modulus, then evaluate the absolute values.

Related tags

Relations And FunctionsStandard FunctionsModulus FunctionFunction EvaluationReal Valued FunctionsTheir Domain And RangeReal Valued Functions Their Domain And RangeMathematicsClass 11 Mcq
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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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