Find the total number of parallel tangents of `f_1(x)=x^2-x+1a n df_2(x)=x^3-x^2-2x+1.`

Which of the following pairs of expression are defined for the same set of values of x ? f_1(x)=2(log)_2xa n df_2(x)=(log)_(10)x^2 f_1(x)=(log)x_xx^2a n df_2(x)=2 f_1(x)=(log)_(10)(x-2)+(log)_(10)(x-3)a n df_(2(x))=(log)_(10)(x-2)(x-3)dot

Which of the following pairs of expression are defined for the same set of values of x ? f_1(x)=2(log)_2xa n df_2(x)=(log)_(10)x^2 f_1(x)=(log)_xx^2a n df_2(x)=2 f_1(x)=(log)_(10)(x-2)+(log)_(10)(x-3)a n df_(2(x))=(log)_(10)(x-2)(x-3)dot

Find the range of (a) f(x) = x^(2) + 2x + 4 (b) f(x) = 1+x -x^(2)

Find the value of f(1) that the function f(x)= (9(x^(2/3)-2x^(1/3)+1))/((x-1)^(2)), x ne 1 is continuous at x =1

Find domain f(x)=sqrt((2x+1)/(x^3-3x^2+2x))

If 2f(x^2)+3f(1/x^2)=x^2-1 , then f(x^2) is

Find the equation of tangent to the y = F(x) at x = 1 , where F(x) = int_(x)^(x^(3))(dt)/(sqrt(1+t^(2)))

Find the sum to n terms of the sequence (x+1//x)^2,(x^2+1//x)^2,(x^3+1//x)^2, ,

Find the sum to n terms of the sequence (x+1//x)^2,(x^2+1//x)^2,(x^3+1//x)^2, ,

Consider a function defined in [-2,2] f (x)={{:({x}, -2 le x lt -1),( |sgn x|, -1 le x le 1),( {-x}, 1 lt x le 2):}, where {.} denotes the fractional part function. The total number of points of discontinuity of f (x) for x in[-2,2] is: