Let f(x)=x3−sinx+secx , defined in the interval [2,4], then the odd extension of f  in the interval [-4,-2] is given by

f(x)=x3−sinx+secx , 2≤x≤4 , let g(x)  be the odd extension of f(x) , then g(x) ={f(x) : 2≤x≤4−f(−x) : −4≤x≤−2 Therefore, in [−4,−2] , odd extension of f(x)  is given by −{(−x)3−sin(−x)+sec(−x)}=x3−sinx−secx .