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Class 12MathematicsRelations and FunctionsOne-one functionExpert
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On which interval is (f:(0,\infty)\to\mathbb{R}), (f(x)=x+\frac{1}{x}), one-one?

Answer and explanation

Correct answer: \((0,1]\) / ((0,1])

Step 1: (f'(x)=1-\frac{1}{x^2}). Step 2: On ((0,1]), (f'(x)\le0), so the function is strictly decreasing and one-one. Step 3: For such functions, choose one side of the minimum point.

Related tags

Reciprocal ExpressionMonotonicityOne-OneDerivativeOne One FunctionRelations And FunctionsMathematicsClass 12 Mcq
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  1. 1Which statement is true for a one-one function?
  2. 2If (f(2)=5) and (f(3)=5), what can be said about (f)?
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  5. 5If (f:\mathbb{R}\to[0,\infty)) and (f(x)=|x|), what type of function is (f)?
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  9. 9Which example proves that (f(x)=x^2+1) is not one-one on real numbers?
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