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Subjects
Class 12MathematicsRelations and FunctionsOnto functionEasy
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If (f:[1,\infty)\to[0,\infty)), (f(x)=\sqrt{x-1}), choose the correct option about (f).

Answer and explanation

Correct answer: It is onto

Step 1: Since (x\ge1), (x-1\ge0), so the function is defined. Step 2: For every (y\ge0), take (x=y^2+1), then (f(x)=y). Step 3: For square-root functions, square the target value to find a preimage.

Related tags

Square RootOntoPreimageDomainOnto FunctionRelations 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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