Composite functions?: L ? et ? ? )? ? x?3,??g(?x)? sin x? ,?? d ?h? ) ?= ?. a. Eva? luate ?h(g(?/2)). ?b?.? ind h? ? (? )). ? ? c?. ? ind ? (? ? (? ))). d. Find the ? domain of ?g ° ? f. e. Fin?d the range of ?f ° ?g.

Step-by-step solution 15RE Step 1 a) We need to evaluate h(g( )) given that g(x) = sin x and h(x) = x. 2 Step 2 Using the definition of a composite function, we have: h(g( )) = h(sin ) [1] 2 2 Step 3 Since sin = 1, equation [1] becomes: 2 h(g(2)) = h(1) [2] Step 4 Applying [2] into the function h, we get: h(g( )) = 1 2 h(g( )2 = 1 Step 5 b) We need to find h(f(x)) given that f(x) = x and h(x) = x. Step 6 Using the definition of a composite function, we have: h(f(x)) = h(x ) [3] Step 7 Applying [3] into the function h, we get: h(f(x)) = x 3 Step 8 c) We need to find f(g(h(x))) given that f(x) = x , g(x) = sin x , and h(x) = x. Step 9 Using the definition of a composite function, we have: f(g(h(x))) = f(g x)) [4] Step 10 Applying [4] into the function g , we get: f(g(h(x))) = f(sinx ) [5]