If `f` is the greatest integer function and `g` is the modulus function, then find the value of `(g0f)(-5/3)-(fog)(-5/3)dot`

If the function f(x)=[((x-2)^3)/a]sin(x-2)+acos(x-2),[dot] denotes the greatest integer function, is continuous in [4,6], then find the values of adot

If f(x) is an even function and satisfies the relation x^2dotf(x)-2f(1/x)=g(x),w h e r eg(x) is an odd function, then find the value of f(5)dot

If f(x)=3x-2 and g(x)=2x+a and if fog=gof , then find the value of a

Let f(x) = ([x]+1)/({x}+1) for f: [0, (5)/(2) ) to ((1)/(2) , 3] , where [*] represents the greatest integer function and {*} represents the fractional part of x. Draw the graph of y= f(x) . Prove that y=f(x) is bijective. Also find the range of the function.

Let f(x)={1+|x|,x<-1[x],xgeq-1 , where [.] denotes the greatest integer function. The find the value of f{f(-2.3)}dot

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^2-1)

If f(x)=3x-2, g(x)=2x+k and if fog=gof, then find the value of k.

Given f(x)=4-(1/2-x)^(2/3),g(x)={("tan"[x])/x ,x!=0 1,x=0 h(x)={x},k(x)=5^((log)_2(x+3)) Then in [0,1], lagranges mean value theorem is not applicable to (where [.] and {.} represents the greatest integer functions and fractional part functions, respectively). f (b) g (c) k (d) h

If f and g are continuous functions with f(3)=5 and lim_(x to 3)[2f(x)-g(x)]=4 , find g(3).