if `f(x)=4x^3-x^2-2x+1` and `g(x)={min f(t): 0<=t<=x; 0<=x<=1, 3-x : 1}` then `g(1/4)+g(3/4)+g(5/4)` is equal to

Let f (x) = x^3-x^2-x+1 and g(x) = {max{f(t); 0<=t<=x}, 0<=x<=1, 3-x, 1<=x<=2 Discuss the continuity and differentiability of the function g (x) in the interval (0, 2).

If f(x) = 2x^(3)-15x^(2)+24x and g(x) = int_(0)^(x)f(t) dt + int_(0)^(5-x) f(t) dt (0 lt x lt 5) . Find the number of integers for which g(x) is increasing.

Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le x,"for",0 le x le 1),(3-x",",1 lt x le 2,,):} Then, g(x) in [0, 2] is

If f(x) =4x^2 and g(x) =f(sin x)+f(cos x), then g (23^(@)) is

If f(x)=x^3+2x^2+3x+4 and g(x) is the inverse of f(x) then g^(prime)(4) is equal to- 1/4 (b) 0 (c) 1/3 (d) 4

If f(x)=x^3+2x^2+3x+4 and g(x) is the inverse of f(x) then g^(prime)(4) is equal to- 1/4 (b) 0 (c) 1/3 (d) 4

If f(x)=4x-5 and g(x)=3^(x) , then f(g(2)) =

Let f(x) = x^(2) + 2x +5 and g(x) = x^(3) - 1 be two real functions. Find (f+g)(x), (f-g)(x), (fg)(x) and ((f)/(g))(x) .

If g(x)=x^3+x-2 and g(f(x))=x^3+3x^2+4x then f(1)+f(2) is equal to ________

If f(x)=x^3+4x^2-x , find f(A) , where A=[(0 ,1, 2 ),(2,-3 ,0),( 1,-1 ,0)] .