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Subjects
Class 12MathematicsRelations and FunctionsOne-one functionHard
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If (g\circ f) is one-one, which statement about (g) is correct?

Answer and explanation

Correct answer: (g) need not be one-one

Step 1: (g\circ f) only uses the behavior of (g) on the range of (f). Step 2: (g) may fail to be one-one on its full domain but still behave distinctly on the range of (f). Step 3: In composition questions distinguish the whole domain from the used part.

Related tags

CompositionInjectivityOne-One FunctionConceptualOne 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)?
  3. 3If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=2x+1), what type of function is (f)?
  4. 4If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=7), what type of function is (f)?
  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?
  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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