Let `f(x)={x^2-4x+3,x<3x-4,xgeq3` `a n dg(x)={x-3,x<4x^2+2x+2,xgeq4` then which of the following is/are true? (a)`(f+g)(3. 5)=0` (b)`f(g(3))=3` (c)`(fg)(2)=1` (d) `(f-g)(4)=0`

Let f(x)=x^2-2x-1 AA x in R Let f:(-oo, a]->[b, oo) , where a is the largest real number for which f(x) is bijective. If f : R->R , g(x) = f(x) + 3x-1 , then the least value of function y = g(|x|) is

Let f(x)={-x^2,for x x^2+8,for x geq 0 the x intercept of the line, that is, the tangent to the graph of f(x) , is zero (b) -1 (c) -2 (d) -4

Let f(x)=|x^2-3x-4|,-1lt=xlt=4 Then f(x) is monotonically increasing in [-1,3/2] f(x) monotonically decreasing in (3/2,4) the maximum value of f(x)i s(25)/4 the minimum value of f(x) is 0

Let f(x) =4x^2-4ax+a^2-2a+2 be a quadratic polynomial in x,a be any real number. If x-coordinate of vertex of parabola y =f(x) is less than 0 and f(x) has minimum value 3 for x in [0,2] then value of a is

Let P(x) = 4x^(2) - 3x + 2x^(3) + 5 and q(x) = x^(2) + 2x + 4 find p ( x) - q(x) .

Let f(x)={x+1,x >0 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

Let f(x)=1/x^2 int_0^x (4t^2-2f'(t))dt then find f'(4)

Let f(x) = max. {|x^2 - 2| x ||,| x |} then number of points where f(x) is non derivable, is :

Let f(x)=30-2x -x^3 , the number ofthe positive integral values of x which does satisfy f(f(f(x)))) gt f(f(-x)) is