Consider a function `y=f(x)` defined implicitly as `2^(x)+2^(y)=2` ,then the domain of f(x)

Consider the function y=f(x) defined implicitly by the equation y^3-3y+x=0 on the interval (-oo, -2)uu(2,oo) . The area of the region bounded by the curve y=f(x) , the x-axis and the lines, x=a, x = b , where -oo lt a lt b lt -2 is (A) int_a^b x/(3((f(x))^2-1))dx+b f(b)-a f(a) (B) -int_a^b x/(3((f(x))^2-1))dx+b f(b)-a f(a) (C) int_a^b x/(3((f(x))^2-1))dx+b f(b)+a f(a) (D) -int_a^b x/(3((f(x))^2-1))dx-b f(b)+a f(a)

If domain of y=f(x) is xin[-3,2] , then the domain of f([x]) is

If f is a real function defined by f(x)=(log(2x+1))/(sqrt3-x) , then the domain of the function is

Consider the function defined implicitly by the equation y^3-3y+x=0 on various intervals in the real line. If x in (-oo,-2) uu (2,oo) , the equation implicitly defines a unique real-valued defferentiable function y=f(x) . If x in (-2,2) , the equation implicitly defines a unique real-valud diferentiable function y-g(x) satisfying g_(0)=0 . If f(-10sqrt2)=2sqrt(2) , then f"(-10sqrt(2)) is equal to

Consider the function defined implicitly by the equation y^3-3y+x=0 on various intervals in the real line. If x in (-oo,-2) uu (2,oo) , the equation implicitly defines a unique real-valued defferentiable function y=f(x) . If x in (-2,2) , the equation implicitly defines a unique real-valued diferentiable function y-g(x) satisfying g_(0)=0 . int_(-1)^(1)g'(x)dx is equal to

Consider the function defined implicitly by the equation y^3-3y+x=0 on various intervals in the real line. If x in (-oo,-2) uu (2,oo) , the equation implicitly defines a unique real-valued defferentiable function y=f(x) . If x in (-2,2) , the equation implicitly defines a unique real-valud diferentiable function y-g(x) satisfying g_(0)=0 . The area of the region bounded by the curve y=f(x) , the X-axis and the line x=a and x=b , where -oo lt a lt b lt -2 is

Consider the function y=f(x) satisfying the condition f(x+1/x)=x^2+1//x^2(x!=0)dot Then the (a) domain of f(x)i sR (b)domain of f(x)i sR-(-2,2) (c)range of f(x)i s[-2,oo] (d)range of f(x)i s(2,oo)

Consider the function f(x)=(.^(x+1)C_(2x-8))(.^(2x-8)C_(x+1)) Statement-1: Domain of f(x) is singleton. Statement 2: Range of f(x) is singleton.

Consider a real-valued function f(x)= sqrt(sin^-1 x + 2) + sqrt(1 – sin^-1x) then The domain of definition of f(x) is

If a function y=f(x) is defined as y=(1)/(t^(2)-t-6)and t=(1)/(x-2), t in R . Then f(x) is discontinuous at