38 Functions and Relations Lesson #5: Composition of Functions A composite function h(x) is given. Use the methods of Class Ex. #1 to complete the diagram, and write h(x) as a composition of two functions, f and g, where h(x) = (f(x)) a) h(x) = (x - 5) 2 g (x) = Ax) = 8( _ b) h(x ) =x3 + 6 Ax) = 8 (x) = g ( ) = c) h(x) = V(x-4) Ax ) = X-4 8 ( x 4 ) =V(-4) 8 (x) = _ X 4. A composite function h(x) is given. In each case, complete the diagram and write h(x) as a composition of two functions, f and g, where h(x) = Ag(x)). a) h(x) = Vx - 4 8 (x) = Ax) = b) h(x) = 1 x + 3 8 (x) = Ax) = 5. Consider two functions f(x) = x + 2 and g(x) = x2. a) Complete the diagram to determine a formula for the composite function h(x) = g(f(x)). x h(x) = 8(f(x)) = 8( b) Use a similar technique to determine a formula for the composite function k(x) = A(g(x)