[ C-1.,f(x)=x+1/x,x!=0 is increasing when ,(1)|x|lt1,(2)|x|gt1, (3) |x|lt2, (4) |x|gt2]

Function f(x) = |x| - |x - 1| is monotonically increasing when a) x lt 0 b) x gt 1 c) x lt 1 d) 0 lt x lt 1

2x-y gt 1, x-2y lt -1

2x-y gt 1, x-2y lt -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 .

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 .

f(x) = {((2x+1), x lt 1),(2,x=1),(x^(2)+1, x gt 1):} is

f(x) = {((2x+1), x lt 1),(2,x=1),(x^(2)+1, x gt 1):} is

A function f(x) is defined as follows : f(x)=x," when "x lt1 =x+1," when "x gt1 =3/2," when "x=1 Draw the graph of f(x) and examine its continuity at x=(1)/(2)and x=1.

If f(x) = {{:(-x, " when "x lt 0),(x^(2), " when "0 le x le 1),(x^(3) -x+1, " when " x gt 1):} then f is differentiable at