If `f(x)={(ln x).sgn({x-1/2});1 < x le 3 and {x^2};3 < x le 3.5.` Find the pointswhere the continuity of `f(x),` should be checked, where [.] is greatest integer function and {.} fractional part function.

If f(x)=x^3sgn(x), then

Discuss the continuity of f(x)=(log|x|)sgn(x^2-1),x!=0.

Determine whether the following functions are even or odd. {:((i)f(x)=log(x+sqrt(1+x^(2))),(ii)f(x)=x((a^(x)+1)/(a^(x)-1))),((iii)f(x)=sinx+cosx,(iv)f(x)=x^(2)-abs(x)),((v)f(x)=log((1-x)/(1+x)),(vi)f(x)={(sgn x)^(sgnx)}^(n)," n is an odd integer"):} {:((vii) f(x)=sgn(x)+x^(2),""),((viii)f(x+y)+f(x-y)=2f(x)*f(y)," where " f(0) ne 0 and x","y ne R.,""):}

if f(x) = tan^(1) x -(1//2) ln x. then

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

If f(x) = x/(1 + (In x)(ln x). ..oo) AA x in [1.oo) then int_1^(2e) f(x) dx equals:

The function f(x)=[log (x-1)]^(2) (x-1)^(2) has :

Discuss continuity of (i) f(x) = sgn(x^(3)-x) (ii) f(x) = sgn(2 cos x-1) (iii) f(x) = sgn(x^(2)-2x+3)

If f(x)=sgn(cos 2x - 2 sin x + 3) , where sgn () is the signum function, then f(x)

f(x)=x sgn (x^(2)) should be