Let `f(x)={x+1,x >0 2-x ,xlt=0` and `g(x)={x+3,x<1,x^2-2x-2,1lt=x<2x-5,xgeq2` Find the LHL and RHL of `g(f(x))` at `x=0` and, hence, fin `lim_(x->0)g(f(x)).`

Let f(x)={x+1,x>0 and 2-x,x<=0g(x)={x+3,x<1 and x^(2)-2x-2,1<=x<2 and x-5

Let f(x)={x+1,x>02-x,x =2 Find the LHL and RHL of g(f(x)) at x=0 and,hence,fin lim_(x rarr0)g(f(x))

Let f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f ('(x)) ^(2). Let n be the numbers of rreal roots of g(x) =0, then:

Let g(x) = 1 + x – [x] and f(x)={:{(-1,if,xlt0),(0,if, x=0),(1,if,x gt0):} then Aax, fog(x) equals (where [ * ] represents greatest integer function).

Let f(x)=x^(3)+x be function and g(x)={(f(|x|)",", x ge 0),(f(-|x|)",",x lt 0):} , then

Let f(x)={1-|x|,|x|<=1 and 0,|x|<1 and g(x)=f(x-)+f(x+1) ,for all x in R .Then,the value of int_(-3)^(3)g(x)dx is

Let f(x) = -x^(3) + x^(2) - x + 1 and g(x) = {{:(min(f(t))",",0 le t le x and 0 le x le 1),(x - 1",",1 lt x le 2):} Then, the value of lim_(x rarr 1) g(g(x)) , is........ .

Let f(x)={x-1,-1<=x<0 and x^(2),0<=x<=1,g(x)=sin x and h(x)=f(|g(x)|)+[f(g(x)) Then

Let f(x)={{:(x sin.(1)/(x)",",x ne0),(0",",x=0):}} and g(x)={{:(x^(2)sin.(1)/(x)",", x ne 0),(0",", x=0):}} Discuss the graph for f(x) and g(x), and evaluate the continuity and differentiabilityof f(x) and g(x).