(b) Let g(x)= `x^2-2` `-ooltxlt0`, `x``0lt x lt 2(x - 2)^2, 2<=xlt4 :(x-4), 4<=xltoo`If the equation g(x)=k has four real and distinct roots, then find the sum of all possible integral valuesof k.

If f''(x) gt 0 AA x in R, f'(4) = 0 and g(x) = f ( cot^2 x - 2 cot x + 5) , 0 lt x lt (pi)/(2) , then

a#b=(-1)^(ab)(a^(b)+b^(a)) f(x)=x^(2)-2x if x ge 0 =0if x lt0 g(x)=2x, if x ge0 =1, if x lt0 Find the value of f(g(2#3))+g(f(1#2)):

a#b=(-1)^(ab)(a^(b)+b^(a)) f(x)=x^(2)-2x if x ge 0 =0if x lt0 g(x)=2x, if x ge0 =1, if x lt0 Find the value of f(2#3)#g(3#4) :

Let f(x) = {:{( sin x +cos x, 0 lt x lt (pi)/(2) ),( a, x = pi//2) , ( tan ^(2) x + cosecx , pi//2lt xlt pi ):} then its odd extension is

Suppose y=f(x) and y=g(x) are two continuous functiond whose graphs intersect at the three points (0,4),(2,2) and (4,0) with f(x) gt g(x) for 0 lt x lt 2 and f(x) lt g(x) for 2 lt x lt 4 . If int_0^4[f(x)-g(x)]dx=10 and int_2^4[g(x)-f(x)]dx=5 the area between two curves for 0 lt x lt 2 ,is (A) 5 (B) 10 (C) 15 (D) 20

Suppose y=f(x) and y=g(x) are two continuous functiond whose graphs intersect at the three points (0,4),(2,2) and (4,0) with f(x) gt g(x) for 0 lt x lt 2 and f(x) lt g(x) for 2 lt x lt 4 . If int_0^4[f(x)-g(x)]dx=10 and int_2^4[g(x)-f(x)]dx=5 the area between two curves for 0 lt x lt 2 ,is (A) 5 (B) 10 (C) 15 (D) 20

Let f (x)= {{:(x ^(2),0lt x lt2),(2x-3, 2 le x lt3),(x+2, x ge3):} then the tuue equations:

Let f (x)= {{:(x ^(2),0lt x lt2),(2x-3, 2 le x lt3),(x+2, x ge3):} then the tuue equations:

Suppose y=f(x) and y=g(x) are two continuous functiond whose graphs intersect at the three points (0,4),(2,2) and (4,0) with f(x) gt g(x) for 0 lt x lt 2 and f(x) lt g(x) for 2 lt x lt 4. If int_0^4[f(x)-g(x)]dx=10 and int_2^4[g(x)-f(x)]dx=5 the area between two curves for 0 lt x lt 2,is (A) 5 (B) 10 (C) 15 (D) 20