Let `f (x) = {{:(2-|x ^(2) +5x +6|, x ne -2),( b ^(2)+1, x =-2):}`
Has relative maximum at `x =-2,` then complete set of values b can take is:

Let f (x = {{: ((x^(2) - 4x + 3)/(x^(2) + 2x - 3), x ne 1),(k, x = 1):} If f (x) is continuous at x= 1, then the value of k will be

Let f(x) = {(|x^(2)-2x| +a",",0 le x lt 5//2),(-2 x + 5",",x ge 5//2):} . If f(x) has a maximum at x= 5/2, then the greatest value of |a| is

If f(x)={{:(,(|x+2|)/(tan^(-1)(x+2)),x ne -2),(,2, x=-2):} , then 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

If (x^(2)-5x+12)/(x^(2)-4x+5)>3, then the complete set of values of x

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then