The largest interval in which the function f(x)=3sin(π216−x2)  assumes values is :

f  is defined only if π216−x2≥0 i.e. x2≤π216⇒x≤π4  or x≥−π4 ⇒−π4≤x≤π/4 .Since f(−π/4)=0,f(π/4)=0  and f(0)=3sinπ4=32 .∴  f takes values in the interval [0,32] .