Given `f(x)={(x^(2)-4|x|+a ,if, x le 2),(6-x, if, x gt 2):}` ,then number of positive integral values of `a` for which `f(x)` has local minima at `x=2` .

Let f(x)={x^(2)-2|x|+a,x<=1 and 6+x,x<1 number of positive integral value(s) of 'a' forwhich f(x) has local minima at x=1 is/are

If f(x)={:{(x+2", if " x le 4),(x+4", if " x gt 4):} , then

f(x)={{:(1+x, if x le 2),(5-x,ifx gt 2):} at x = 2 .

f(x){{:(x^(3) - 3"," if x le 2 ),(x^(2) + 1"," if x gt 2 ):}

(x)/(2)+(2)/(x) has local minima at

If f(x)={(ax+3",",x le 2),(a^(2)x-1"," , x gt 2):} , then the values of a for which f is continuous for all x are

If f(x) = {(kx^(2),"if"x le 2),(3,"if" x gt 2):} is continuous at x = 2, then the value of k is

Let f(x)=30-2x-x^(3), the number ofthe positive integral values of x which does satisfy f(f(f(x)))>f(f(-x)) is

Let f (x) = {{:( x^(3) - x^(2) + 10 x- 5 , "," , x le 1), ( -2x + log _(2) (b^(2) - 2) , "," , x gt 1):} the set of values of b for which f(x) has greatest value at x = 1 is given by