AP EAMCET202319 May 2023Morning ShiftMathematicsDifferentiationActual
If f(x) is differentiable on R , f(x) f^ (-x)-f(-x) f^ (x)=0 , f(x) f^ (-x)=0, f(0)=3 and f(3)=9 , then (1+f(-3))^3+1=
Options
- A2
- B9
- C28
- D0
Correct answer
B. 9
Step-by-step solution
Given, f(x) f^ (-x)-f(-x) f^ (x)=0 f(-x) f^ (x)-f^ (-x) f(x)=0 d d x [f(-x) f(x)]=0 f(-x) f(x)=c where c= Arbitrary constant when x=0 , then f(0) f(0)=c c=9 when x=3 , then aligned & f(-3) f(3)=c f(-3) .(9)=9 & f(-3)=1 aligned Now [1+f(-3)]^3+1=[1+1]^3+1=9