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Most Important Selected Qs for JEE AdvancedMathematicsFunctions

Consider, f(f(x-2))= (x^2+3 )^2+1 x R . Identify which of the following statement(s) is(are) correct?

Options

  1. ALeast value of f(x) is 1
  2. BLeast value of f(x) is 10
  3. C. d(f(f(x))) d x |_ x=0 =56
  4. DIf d x f(x) =g(x)+C where C is a constant and g(-2)=0 , then g(0)+g(1)= 3 4

Correct answer

D. If d x f(x) =g(x)+C where C is a constant and g(-2)=0 , then g(0)+g(1)= 3 4

Step-by-step solution

f(f(x-2))= (x^2+3 )^2+1x-2 t array ll & f(f(t))= ((t+2)^2+3 )^2+1= (t^2+4 t+7 )^2+1= (t^2+4 t+5+2 )^2+1 & f(f(t))= (t^2+4 t+5 )^2+4 (t^2+4 t+5 )+5 & f(x)=x^2+4 x+5 array (1) f(x)=(x+2)^2+1 Least value of f(x) is 1 . (3) d(f(f(x))) d x =2 ((t+2)^2+3 ) (2(t+2)) . d(f(f(x))) d x |_ x=0 =2 7 4=56 (4) d x (x+2)^2+1 = ⁻¹(x+2)+C g(x)= ⁻¹(x+2) g(0)+g(1)= ⁻¹ 2+ ⁻¹ 3= 3 4

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