Two functions are defined as under, `f(x)={(x+1, x le1),(2x+1, 1ltxle2):}` `g(x)={(x^2, -1lexlt2),(x+2, 2lexle3):}`
Find fog and gof

If f(x)={(3x^2+12x-1,-1lexle2),(37-x,2ltxle3):}

If f(x)={(x[x], 0lexlt2),((x-1)[x],2lexle3):} , then f(x) is

If f(x)={(4, -3ltxlt-1),(5+x, -1lexlt0),(5-x, 0 lexlt2),(x^2+x-3, 2lexlt3):} then f(IxI) is

The function f:R->[-1/2,1/2] defined as f(x)=x/(1+x^2) is

If f(x) ={(x^(3)", " x lt1),(2x-1", " x ge 1):} " and " g(x)={(3x", " x le2),(x^(2)", " x gt 2):} " then find " (f-g)(x).

If the function f(x) ={x+1 if x le 1 , 2x+1 if 1 lt x le 2 and g(x) = {x^2 if -1 le x le 2 , x+2 if 2 le x le 3 then the number of roots of the equation f(g(x))=2

A continuous function f(x) is defined as follows : f(x)={{:(x,"when "xlt1),(ax+bx^(2),"when "1lexle2),(2x^(2),"when "xgt2):} Find the values of a and b.

Consider two functions y=f(x) and y=g(x) defined as f(x)= {[a x^2 +b, 0lexle1],[ bx + 2b, 1ltxle3],[(a-1)x + 2c - 3 , 3ltxle4]} And g(x)={[c x + d , 0le x le 2],[a x+3-c ,2ltxlt3],[x^2+b+1,3lexle4]} Let f be differentiable at x=1a n dg(x) be continuous at x=3. If the roots of the quadratic equation x^2+(a+b+c)alphax+49(k+kalpha)=0 are real distinct for all values of alpha then possible value of k will be a) k in (-1,0) b). k in (oo,0) c). k in (1,5) d). k in (-1,1)

Let f(x) be defined on [-2,2] and is given by f(x)={(-1, -2lexlt0),(x-1, 0lexle2):} and g(x)=f(|x|)+|f(x)|, then find g(x).

Consider two function y=f(x) and y=g(x) defined as f(x)={{:(ax^(2)+b,,0lexle1),(bx+2b,,1ltxle3),((a-1)x+2c-3,,3ltxle4):} and" "g(x)={{:(cx+d,,0lexle2),(ax+3-c,,2ltxle3),(x^(2)+b+1,,3ltxle4):} underset(xrarr2)(lim)(f(x))/(|g(x)|+1) exists and f is differentiable at x = 1. The value of limit will be