Most Important Selected Qs for JEE AdvancedMathematicsFunctions

Let f(x) be a monic polynomial of degree 5 . The graph of |f(x)| and f(|x|) are same. If f(2)=0 . Then:

Options

AThe value of f(0)+f(1) equals 25
Bf(x)+f(-x)=0 x R
C_ x 2 (1+f(x))^ 1 1- (x-2) equals e⁶⁴
D( x f(x) )^ 1 4 d x= (x+ x^2-4 )+C where C is constant of integration

Correct answer

D. ( x f(x) )^ 1 4 d x= (x+ x^2-4 )+C where C is constant of integration

Step-by-step solution

If graph of |f(x)| and f(|x|) is same then f(x)>0 x>0 Given f(2)=0 f^ (2)=0 because f(x) cannot be -ve for x>0 . By symmetry f(-2)=f^ (-2)=0 f(x)=x(x-2)^2(x+2)^2 (Note: Function must be odd) f(x)=x (x^2-4 )^2

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