In the questions, `[x]a n d{x}` represent the greatest integer function and the fractional part function, respectively. If `y=3[x]+1=4[x-1]-10 ,` then find the value of `[x+2y]dot`

In the question, [x]a n d{x} represent the greatest integer function and the fractional part function, respectively. Solve: [x]^2-5[x]+6=0.

Solve 2[x]=x+{x},w h r e[]a n d{} denote the greatest integer function and the fractional part function, respectively.

Solve : [x]^(2)=x+2{x}, where [.] and {.} denote the greatest integer and the fractional part functions, respectively.

Solve : 4{x}= x+ [x] (where [*] denotes the greatest integer function and {*} denotes the fractional part function.

Solve (x-2)[x]={x}-1, (where [x]a n d{x} denote the greatest integer function less than or equal to x and the fractional part function, respectively).

If f(x) = [x] , 0<= {x} < 0.5 and f(x) = [x]+1 , 0.5<{x}<1 then prove that f (x) = -f(-x) (where[.] and{.} represent the greatest integer function and the fractional part function, respectively).

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

Draw the graph of |y|=[x] , where [.] represents the greatest integer function.

Find the value of int_(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denote the greatest function and fractional parts of x , respectively.