" If "f(x)={[2x+b(x=a)]" is such that "Ltquad f(x)=1" then "l=

If f(x)= {{:(,2x+b,(x lt a)),(,x+d,(x ge a)):}" is such that " underset(x to a)"Lt" f(x)="l then l="

If f(x) = {(2x+b, x lt alpha),(x+d, x gea):} is such that lim_(x rarr alpha) f(x) = l , then l =

Statement-1 : The function f defined as f(x) = a^(x) satisfies the inequality f(x_(1)) lt f(x_(2)) for x_(1) gt x_(2) when 0 lt a lt 1 . and Statement-2 : The function f defined as f(x) = a^(x) satisfies the inequality f(x_(1)) lt f(x_(2)) for x_(1) lt x_(2) when a gt 1 .

Statement-1 : The function f defined as f(x) = a^(x) satisfies the inequality f(x_(1)) lt f(x_(2)) for x_(1) gt x_(2) when 0 lt a lt 1 . and Statement-2 : The function f defined as f(x) = a^(x) satisfies the inequality f(x_(1)) lt f(x_(2)) for x_(1) lt x_(2) when a gt 1 .

If f (x) = sin (2x ^(2) -2 [x]) for 0 lt x lt 1, then f ' ((sqrtpi)/(2))=

If f (x) ={{:(x",", "when " 0 lt x lt 1),(2-x",", "when" 1 lt x le 2):} then f'(1) is equal to-

Suppose f(x)={{:(a+bx,if x lt 1),(4, if x =1),(b-ax, ifx gt 1):} If Lt_(x to 1-)f(x)=f(1), Lt_(x to 1+)f(x)=f(1) then find the possible values of a and b.