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Class 12MathematicsRelations and FunctionsFunctionsExpert
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If (f:A\to B) is bijective, what is (f^{-1}\circ f) equal to?

Answer and explanation

Correct answer: (I_A)

Step 1: First, (f) sends an element of (A) to (B). Step 2: Then (f^{-1}) brings it back to the original element. Step 3: Therefore (f^{-1}\circ f) is the identity function on (A).

Related tags

FunctionsInverseIdentityCompositionRelations And FunctionsMathematicsClass 12 Mcq
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  1. 1If (f:A\to B) is a function, what condition is necessary for every element of (A)?
  2. 2If (f(x)=2x+3), what is the value of (f(4))?
  3. 3In a function (f:A\to B), what is (A) called?
  4. 4In a function (f:A\to B), what is (B) called?
  5. 5If (f={(1,2),(2,4),(3,6)}), what is the domain of (f)?
  6. 6If (f={(1,2),(2,4),(3,6)}), what is the range of (f)?
  7. 7Which of the following relations from (A={1,2}) to (B={3,4}) is a function?
  8. 8If (f(x)=x^2) and the domain is ({-2,-1,0,1,2}), what is the range?
  9. 9For the function (f:R\to R), (f(x)=x+5), what is (f(0))?
  10. 10If f(x) = 3x − 1, what is the value of f(2) + f(0)?
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