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Class 12MathematicsRelations and FunctionsFunctionsHard
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If (f(x)=3x-1) and (g(x)=\frac{x+1}{3}), what kind of function is (g\circ f)?

Answer and explanation

Correct answer: Identity function

Step 1: ((g\circ f)(x)=g(3x-1)). Step 2: (g(3x-1)=\frac{3x-1+1}{3}=x). Step 3: A function that gives (x) for every (x) is the identity function.

Related tags

Identity-FunctionCompositionInverseFunctionsRelations 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?
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  10. 10If f(x) = 3x − 1, what is the value of f(2) + f(0)?
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