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Subjects
Class 12MathematicsRelations and FunctionsOne-one functionHard
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If (f:A\to B) and (g:B\to C) are both one-one, what is the correct statement about (g\circ f)?

Answer and explanation

Correct answer: (g\circ f) is one-one

Step 1: Assume ((g\circ f)(x_1)=(g\circ f)(x_2)). Step 2: Since (g) is one-one, (f(x_1)=f(x_2)), and since (f) is one-one, (x_1=x_2). Step 3: The composition of two one-one functions is one-one.

Related tags

Composition Of FunctionsInjective FunctionOne-One FunctionClass 12One One FunctionRelations And FunctionsMathematicsClass 12 Mcq
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10 more MCQs
  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?
  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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