If f={(a,0),(b,2),(c,-3)} and g={(a,-1),(b,1),(c,2)} then find `f^2+g^2`

Let S = {a , b , c}" and "T = {1, 2, 3} . Find F^(-1) of the following functions F from S to T, if it exists.(i) F = {(a , 3), (b , 2), (c , 1)} (ii) F = {(a , 2), (b , 1), (c , 1)}

If f(a,b) =(f(b)-f(a))/(b-a) and f(a,b,c)=(f(b,c)-f(a,b))/(c-a) prove that f(a,b,c)=|{:(f(a),f(b),f(c)),(1,1,1),(a,b,c):}|-:|{:(1,1,1),(a,b,c),(a^(2),b^(2),c^(2)):}| .

If f(x), g(x) be twice differentiable function on [0,2] satisfying f''(x)=g''(x) , f'(1)=4 and g'(1)=6, f(2)=3, g(2)=9, then f(x)-g(x) at x=4 equals to:- (a) -16 (b) -10 (c) -8

Let A = {1,2,3,4} and f : A to A satisfy f (1) =2, f(2)=3, f(3)=4, f (4)=1. Suppose g:A to A satisfies g (1) =3 and fog = gof , then g = (a).{(1,3), (2,1), (3,2), (4,4)} (b).{(1,3), (2,4),(3,1),(4,2)} (c).{(1,3),(2,2),(3,4),(4,3)} (d).{(1,3),(2,4),(3,2),(4,1)}

If f(x)=2/(x-3),g(x)=(x-3)/(x+4) , and h(x)=-(2(2x+1))/(x^2+x-12) then lim_(x->3)[f(x)+g(x)+h(x)] is (a) -2 (b) -1 (c) -2/7 (d) 0

If a ,b ,c ,d are in G.P. prove that: (a^2+b^2),(b^2+c^2),(c^2+d^2) are in G.P. (a^2-b^2),(b^2-c^2),(c^2-d^2) are in G.P. 1/(a^2+b^2),1/(b^2+c^2),1/(c^2+d^2) are in G.P.

If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of lim_(x->a)(g(x)f(a)-g(a)f(x))/(x-a) is (a) -5 (b) 1/5 (c) 5 (d) none of these

Let f(x)={(-,1, -2lexlt0),(x^2,-1,0lexlt2):} if g(x)=|f(x)|+f(|x|) then g(x) in (-2,2) is (A) not continuous is (B) not differential at one point (C) differential at all points (D) not differential at two points

If f and g are differentiable functions in [0, 1] satisfying f(0)""=""2""=g(1),g(0)""=""0 and f(1)""=""6 , then for some c in ]0,""1[ (1) 2f^'(c)""=g^'(c) (2) 2f^'(c)""=""3g^'(c) (3) f^'(c)""=g^'(c) (4) f'(c)""=""2g'(c)

If f and g are differentiable functions in [0, 1] satisfying f(0)""=""2""=g(1),g(0)""=""0 and f(1)""=""6 , then for some c in ]0,""1[ (1) 2f^'(c)""=g^'(c) (2) 2f^'(c)""=""3g^'(c) (3) f^'(c)""=g^'(c) (4) f'(c)""=""2g'(c)