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)).`

If f(x)={x/(s in x),x >0 2-x ,xlt=0 and g(x)={x+3,x<1x^2-2x-2,1lt=x<2x-5,xgeq2 Then the value of (lim)_(xvec0)g(f(x)) a. is -2 b. is -3 c. is 1 d. does not exist

Let f(x)={{:(x+1", "xlgt0),(2-x", "xle0):}"and"g(x)={{:(x+3", "xlt1),(x^(2)-2x-2", "1lexlt2),(x-5", "xge2):} Find the LHL and RHL of g(f(x)) at x=0 and, hence, find lim_(xto0) 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

If f(x)={x-1,xgeq1 2x^2-2,x 0-x^2+1, xlt=0,and h(x)=|x| ,t h e n("lim")_(xvec0)f(g(h(x))) is___

f( x )={ x+1,x 0 and g(x)={ x 3 x 1 find f(g(x)) and its domain and range

Let f(x) be defined on [-2,2] and be given by f(x) = -1 , -2 <= x <= 0 1-x , 0 <= x <= 2 . and g(x)=f(|x|)+|f(x)|dot Then find g(x)dot

Let f(x)=(g(x))/x w h e nx!=0 and f(0)=0. If g(0)=g^(prime)(0)=0a n dg^(0)=17 then f(0)= 3//4 b. -1//2 c. 17//3 d. 17//2

If f(x)={{:((x)/(sinx)",",x gt0),(2-x",",xle0):}andg(x)={{:(x+3",",xlt1),(x^(2)-2x-2",",1lexlt2),(x-5",",xge2):} Then the value of lim_(xrarr0) g(f(x))

Let g(x)=1+x-[x] and f(x)={-1,x 0. Then for all x,f(g(x)) is equal to (where [.] represents the greatest integer function). (a) x (b) 1 (c) f(x) (d) g(x)

If f(x)={1-|x|,|x|lt=1 0,|x|>1'a n dg(x)=f(x-1)+f(x+1), find the value of int_(-3)^3g(x)dxdot