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.

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

Let f(x)={(log(1+x)^(1+x)-x)/(x^2)}dot Then find the value of f(0) so that the function f is continuous at x=0.

Discuss the differentiability of f(x)=|x|sinx+|x-2|sgn(x-2)+|x-3|dot

Which of the following functions is one-one ? (1)f:R->R defined as f(x)=e^(sgn x)+e^(x^2) (2) f:[-1,oo) ->(0,oo) defined by f(x)=e^(x^2+|x|) (3)f:[3,4]->[4,6] defined by f(x)=|x-1|+|x-2|+|x-3|+x-4| (4) f(x) =sqrt(ln(cos (sin x))

The domain of the function f(x)=(log)_(3+x)(x^2-1) is

If f(x)=(log)_e((x^2+e)/(x^2+1)) , then the range of f(x)

If f(x)=sin(log)_e{(sqrt(4-x^2))/(1-x)} , then the domain of f(x) is _____ and its range is __________.

Find the extrema of f(x) = log (1 + x)- (x)/(1 + x), x gt -1

Draw the graph of the function y= f(x) = lim_(n to oo) (x^(2n)-1)/(x^(2n)+1) . Is this function same as the function g(x) = "sgn"(x^(2)-1) .

If f(x)={xcosx+(log)_e((1-x)/(1+x))a; x=0; x!=0 is odd, then a_______,