Question

For each pair of functions f and g below, find f(g(x)) and g(x)). Then, determine whether f and g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (a) f(x) = -,x0 (b) f(x) = x + 4 $(x) = -,x+0 x 5 ? g(x) = -x + 4 $($(x)) = 0 (g(x)) = 0 g(x)) = 0 g(x)) = 0 of and g are inverses of each other of and g are not inverses of each other of and g are inverses of each other of and g are not inverses of each other

Answer 1

Sol-

f(x) = 2/3 470 } liven that g(x)= 3x -*70 S For f(4m) we know = f(x) = 5) f/8(m) < put x= grey 3) f (gw) = £g(x) } => [f(g(x) = * ] Ane For g (f(x)) ^. We know that = g(x) = 24 o g (fm) a firm {put x=f(my? 5 949) - SAME [g(4m) = * Ans. . The value of the function of (g(x) = g(f(x)} J . f and g are inverse of each other Anf,

(b) f(x) = x+4 ? given 1 7' g(x) = -x+4 For f(g(x)) . We know that ) f(x) = x+4 = f(gas) = g(x)ty & put x = g(x)} 5) f(g(x)) = -x+4+$9(*)=-x+y} f(g(x)) = -x+8 am For g (f(x)) we know that g(x) = -x+4 7 g (f(x)) = -f(x)+4 & put x = f(x) 3) g(fxy) = +(x+4)+4 57189 2 x+y} - Ans. 5) g (f(x)) = -*-474 f(f()) = -* - Ang The value of the function f(g(x) = g(f(x))/ ... f and g are not inverses of s each other Ans.