Let R be a relation such that R={(a,d),(c,g),(d,e),(d,f),(g,f)} then (Ro(R)^(-1))^(-1)" is

Let R be a relation such that R={(a d) (c g) ) (d e) (d f) (g f)} then (R R^(-1))^(-1) is {(d d) (g g) (e e) (f f) (e f) (f e)} {(e a) (f a) (f c)} {(a e) (a f) (c f) {(d d) (g g) (e e) (f f) (e f)}

Let R be a relation such that R={(a d) (c g) (d e) (d f) (g f)} then (R@R^(-1))^(-1) is qquad {(d d) (g g) (e e) (f f) (e f) (f e)} O{(e a) (f a) (f c)} O{(a e) (a f) (c f) O{(d d) (g g) (e e) (f f) (e f)}

Let R be a relation such that R={(a d) (c g) (d e) (d f) (g f)} then (R@R^(-1))^(-1) is qquad {(d d) (g g) (e e) (f f) (e f) (f e)} O{(e a) (f a) (f c)} O{(a e) (a f) (c f) O{(d d) (g g) (e e) (f f) (e f)}

Let R be a relation such that R={(a d) (c g) (d e) (d f) (g f)} then (ROR^(1))^(-1) is

Let R be a relation such that R={(a c) (c g) (d e) (d f) (g f)} then (RoR^(1))^(-1) is O(d d) (g g) (e e) (f f) (e f) (f e)} O {(e a) (f a) (f c)} O {(a e) (a f) (c f) 0 {(d c) (g g) (e e) (f f) (e f)}

If f' is an increasing function from R rarr R such that f''(x)>0 and f^(-1) exists then (d^(2)(f^(-1)(x)))/(dx^(2)) is 0 c.=0 d.cannot be determined

Let f: R-> R, g:R->R and h:R->R be the differential functions such that f(x)=x^3+3x+2, g(f(x))=x and h(g(g(x)))=x, for all x in R. Then (a)g'(2)=1/15 (b)h'(1)=666 (c)h(0)=16 (d)h(g(3))=36

Let f:R rarr R be such that f(1)=3andf'(1)=6. Then lim_(x rarr0)((f(1+x))/(f(1)))^(1/x)=(a)1( b) e^((1)/(2))(c)e^(2) (d) e^(3)

Let f and g be differentiable functions such that: xg(f(x))f\'(g(x))g\'(x)=f(g(x))g\'(f(x))f\'(x) AA x in R Also, f(x)gt0 and g(x)gt0 AA x in R int_0^xf(g(t))dt=1-e^(-2x)/2, AA x in R and g(f(0))=1, h(x)=g(f(x))/f(g(x)) AA x in R Now answer the question: f(g(0))+g(f(0))= (A) 1 (B) 2 (C) 3 (D) 4

Let R be a relation on NxxN defined by (a , b) R(c , d)hArra+d=b+c for a l l (a , b),(c , d) in NxxN show that: (i) (a , b)R (a , b) for a l l (a , b) in NxxN (ii) (a , b)R(c , d)=>(c , d)R(a , b)for a l l (a , b), (c , d) in NxxN (iii) (a , b)R (c , d)a n d (c , d)R(e ,f)=>(a , b)R(e ,f) for all (a , b), (c , d), (e ,f) in NxxN