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Class 12MathematicsRelations and FunctionsOne-one functionExpert
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Which statement is correct about (f:(0,\infty)\to(0,\infty)), (f(x)=\frac{1}{x})?

Answer and explanation

Correct answer: It is one-one

Step 1: Assume (f(a)=f(b)). Step 2: (\frac{1}{a}=\frac{1}{b}) gives (a=b), since (a,b>0). Step 3: For reciprocal-type functions, direct proof using equal images is very effective.

Related tags

Reciprocal FunctionOne-OneDirect ProofDomainOne 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)?
  6. 6If (f:\mathbb{R}\to(0,\infty)) and (f(x)=e^x), what type of function is (f)?
  7. 7If (f:(0,\infty)\to\mathbb{R}) and (f(x)=\log x), which statement about (f) is correct?
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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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