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Subjects
Class 12MathematicsRelations and FunctionsOnto functionHard
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If (f:\mathbb{R}\to(-1,1)) and (f(x)=\frac{x}{1+|x|}), is (f) onto or not?

Answer and explanation

Correct answer: It is onto

Step 1: The range of this function is ((-1,1)). Step 2: For (y\ge0), take (x=\frac{y}{1-y}), and for (y<0), take (x=\frac{y}{1+y}). Step 3: For modulus-based expressions, checking cases separately is helpful.

Related tags

Onto FunctionRange IntervalModulusPreimageRelations And FunctionsMathematicsClass 12 Mcq
सुधार सुझाएँ / Earn

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10 more MCQs
  1. 1If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x+5), which statement about (f) is correct?
  2. 2If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2), why is (f) not onto?
  3. 3If (f:\mathbb{R}\to[0,\infty)), (f(x)=x^2), what is the correct statement about (f)?
  4. 4For sets (A={1,2,3}) and (B={a,b}), (f={(1,a),(2,b),(3,a)}). Choose the correct statement about (f:A\to B).
  5. 5For (A={1,2,3}) and (B={p,q,r}), (f={(1,p),(2,p),(3,q)}). Why is it not onto?
  6. 6If (f:\mathbb{R}\to\mathbb{R}), (f(x)=2x-7), what should (x) be for any (y\in\mathbb{R}) so that (f(x)=y)?
  7. 7If (f:\mathbb{N}\to\mathbb{N}), (f(n)=n+1), why is (f) not onto?
  8. 8If (f:\mathbb{Z}\to\mathbb{Z}), (f(n)=n-3), what is the correct statement about (f)?
  9. 9If (f:\mathbb{Z}\to\mathbb{Z}), (f(n)=2n), why is (f) not onto?
  10. 10If (f:\mathbb{R}\to(0,\infty)), (f(x)=e^x), which statement is correct?
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