`f(x)=2x^3-3x^2-x+3/2` then which of the following is/are incorrect? `int_(1/8)^(7/8)f(f(x))dx=3/4`

Options

A. `int(1//8)^(7//8) f(c(x))dx=3/4`
B. `y=(f(x))^(3//5)` is not differentiabble at exactly 1 point
C. `y=[f(x)+lamda], (lamda in` prime number) is discontinuous at 3 point if `x in [0,1]`
D. `f(f(x))=0` has minimum 6 real roots

Answer

A, B, C

Explanation

`I=int_(1//8)^(7//8)f(f(x))dx`……(1)
`I=int_(1//8)^(7//8)f(f(1-x))dx=int_(1//8)^(7//8)f(1-f(x))dx`…..(2)
So `2I=3/4`