Answer:
Option A,B
Explanation:
f(x)=acos(|x3−x|)+b|x|sin(|x3+x|)
if x3−x≥0
⇒cos|x3−x|=cos(x3−x)
x3−x≤0
⇒cos|x3−x|=cos(x3−x)
∴cos(|x3−x|)=cos(x3−x),∀xϵR .........(i)
Again , if x3+x≥0
⇒|x|sin(|x3+x|)=xsin(x3+x)
x3+x≤0
⇒|x|sin(|x3+x|)=−xsin(−(x3+x))
∴ |x|sin(|x3+x|)=xsin(x3+x),∀xϵR .......(ii)
⇒f(x)=acos(|x3−x|)+b|x|sin(|x3+x|)
∴ f(x)=acos(x3−x)+bxsin(x3+x) ........(iii)
which is clearly sum and composition of differential functions.
Hence, f(x) is always continuous and differentiable