`f(x)={(max(|x|,x^2), |x|le2),(8-2|x|, 2lt|x|le4):}` is (a) discontiuous at `x=1` (b) discontinous at `x=2` (c) non differentiable at `x=2` (d) discontinuous at `x=-1`

If f(x)={{:(,x^(2)+1,0 le x lt 1),(,-3x+5, 1 le x le 2):}

If f(x)={'x^2(sgn[x])+{x},0 Option 1. f(x) is differentiable at x = 1 Option 2. f(x) is continuous but non-differentiable at x = 1 Option 3. f(x) is non-differentiable at x = 2 Option 4. f(x) is discontinuous at x = 2

Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f ^(-1) (x) is discontinous at x=

If the function f(x)={(Ax-B ,, x le 1),(3x ,,1 lt x lt 2),(Bx^2-A ,, x ge 2):} is continuous at x=1 and discontinuous at x=2 , find the values of A and B .

Let f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):} find (fof) (x).

f(x)={:{(5, x le 1) ,(a+bx,1 lt x lt 3),(b+5x,3 le x lt 5),(30,xge5):} then (a) f(x) is discontiuous AA a in R, b in R (b) f(x) is discontiuous if a=0 & b=5 (c) f(x) is discontiuous if a=5 & b=0 (d) f(x) is discontiuous if a=-5 & b=10

If f(x)=x^3(sgn [x] + {x}):0le xlt2, cosx+|x-2| ; 2 le x le pi Where [.], {.} and sgn (.) represents the greatest integer, the fractional part and signmum function respectively A. f(x) is differentiable at x = 1 B) f(x) is continuous but non-differentiable at x = 1 C) f(x) is discontinuous at x= 2 D) f(x) is non-differentiable at x =2

f(x)={(|2x-3|[x],0lexle2),(x^(2)/2,2ltxle3):} . If f(x) is defined in (0,3) then ([.] denotes greatest integer function) A. Point of discontiuity at x=1, 1/2,2 B. Point of discontinuity at x=1 and 2 C. Point of non-differentiability at x=1, 1/2,2 D. Point of non-differentiability at x=1, 3/2, 2

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

If f(x)={:{(3x^2+12x-1"," -1le x le2),(37-x ","2 lt x le 3):} then