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.

f(x)={(ln x)*sgn({x-(1)/(2)});1

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

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

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

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

If f(x)=ln(1+x)-(tan^(-1)x)/(1+x) , (for x> 0) then sgn f(x) is ( sgn represents signum function)

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.,""):}

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)= a^({a^(|x|)sgn x }),g(x)=a^([a^(|x|)sgn x] for a gt 1, a!=1 and x in R , where {**} & [**] denote the fractional part and integral part functions respectively, then which of the following statements holds good for the function h(x) , where (ln a) h(x) = (ln f(x) + ln g(x)) .