if `f(x)=4x^3-x^2-2x+1` and `g(x)={min{f(t): 0<=t<=x; 0<=x<=1, 3-x when1 less x less than or equal 2}` then g(1/4)+g(3/4)+g(5/4) is equal to

Let f(x)=x^3-3x^2+6AAx in R and g(x)={m a x :f(t ; x+1lt=tlt=x+2,-3lt=xlt=0 1-x ,xgeq .Find continuity and differentiability of g(x) for x in [-3,1]

Given that f'(x)=4x^(3)-3x^(2)+2x-1 find f(x) if f(0)=0 .

If f(x) = 2x^(3)+7x-5 and g(x) = f^(-1)(x) , then reciprocal of g^(')(4) is equal to

If f(x)=(x^(2)+3x+2)(x^(2)-7x+a) and g(x)=(x^(2)-x-12)(x^(2)+5x+b) , then the value of a and b , if (x+1)(x-4) is H.C.F. of f(x) and g(x) is

Let f(x)=f_1(x)-2f_2 (x) , where ,where f_1(x)={((min{x^2,|x|},|x|le 1),(max{x^2,|x|},|x| le 1)) and f_2(x)={((min{x^2,|x|},|x| lt 1),({x^2,|x|},|x| le 1)) and let g(x)={ ((min{f(t):-3letlex,-3 le x le 0}),(max{f(t):0 le t le x,0 le x le 3})) for -3 le x le -1 the range of g(x) is

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

Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-f(x))dot Show that g(x)geq0AAx in Rdot

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

If f'(x)=3x^2 -4x+5" and "f(1)=3 , then find f(x) .

If f'(x) = 3x^2 - 4x + 5 and f(1) = 3 then find f(x).