The correct options are
B f(x) is an odd function
C Number of integers in range of f(x) are 4.
sin(sin−12x)=2x for −12≤x≤12
sec(sec−13x)=3x for x≤−13 or x≥13
∴ f(x)=9x for xϵ[−12,−13]∪[13,12]
(A) fog(x)=9g(x)=81x is defined for
g(x)ϵ[−12,−13]∪[13,12]
while gof(x)=9f(x)=81x is defined for
xϵ[−12,−13]∪[13,12]
∴ gof(x) & fog(x) are not equal.
(C) Range of f(x)=[−92,−3]∪[3,92]
⇒ Number of integers=4