यदि `f : X to Y` तथा `g : Y to Z` दो एकेकी आच्छादक प्रतिचित्रण हो तो दिखाए कि `gof : X to Z` एकेकी आच्छादक है। यह भी सिद्ध कीजिए कि `(gof)^(-1) = f^(-1) og^(-1)`

If f:X to Y and g:Y to Z be two bijective functions, then prove that (gof)^(-1) =f^(-1)og(-1) .

If f and g are two bijections; then gof is a bijection and (gof)^(-1)=f^(-1)og^(-1)

If f: X to Y, g : Y to Z and h: Z to S are functions, then ho(gof) = (hog)of .

If f:ArarrB,g:BrarrC are two bijective functions then P.T ("gof")^(-1)=f^(-1)"og"^(-1)

If f: R to R, g : R to R defined by f(x) = 3x-2, g(x) = x^(2)+1 , then find: (i) (gof^(-1))(2) , (ii) (gof)(x-1)

If f(x) = 1/x , g(x) = sqrtx find gof(x)?

Consider f: {1,2,3} to {a,b,c} and g: {a,b,c} to {apple, ball, cat} defined as f (1) =a, f (2) =b, f (3)=c, g (a) = apple, g (b) = ball and g (c )= cat. Show that f, g and gof are invertible. Find out f ^(-1) , g ^(-1) and ("gof")^(-1) and show that ("gof") ^(-1) =f ^(-1) og ^(-1).