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MHT CET202619 April 2026Morning ShiftMathematicsFunctionsActual

If f(x) = x^2 and g(x) = [x^2] where [ ] represents the greatest integer function then, (f g) ( 3 2 ) + (g f) ( 3 2 ) is equal to ...

Options

  1. A2
  2. B5
  3. C9
  4. D10

Correct answer

C. 9

Step-by-step solution

Given f(x) = x^2 and g(x) = [x^2] . First, evaluating (f g) ( 3 2 ) : g ( 3 2 ) = [ ( 3 2 )^2 ] = [ 9 4 ] = [2.25] = 2 f (g ( 3 2 ) ) = f(2) = 2^2 = 4 Next, evaluating (g f) ( 3 2 ) : f ( 3 2 ) = ( 3 2 )^2 = 9 4 g (f ( 3 2 ) ) = g ( 9 4 ) = [ ( 9 4 )^2 ] = [ 81 16 ] = [5.0625] = 5 Adding both values: (f g) ( 3 2 ) + (g f) ( 3 2 ) = 4 + 5 = 9 Answer: 9

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