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Class 12MathematicsRelations and FunctionsOne-one functionExpert
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If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^3-3x), on which interval is the function one-one?

Answer and explanation

Correct answer: One-one on ((-\infty,-1])

Step 1: Check monotonic behaviour to test one-one nature. Step 2: (f'(x)=3x^2-3=3(x-1)(x+1)), so the function is increasing on ((-\infty,-1]). Step 3: In exams, the sign of the derivative is the quickest method for such cubic functions.

Related tags

One-One FunctionMonotonicityDerivativeRelations And FunctionsOne One FunctionMathematicsClass 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)?
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  8. 8If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=3x-5), what follows from (f(a)=f(b))?
  9. 9Which example proves that (f(x)=x^2+1) is not one-one on real numbers?
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