If f(x) = and g(x) = x3 ? 2, find the compositions f ° g, g ° f, f ° f, and g ° g.

Step-by-step solution Step 1 of 4 Consider two given function and To find the composition of the function mean So, put the value of g(x) in place o in the function f(x). Next step, obtain And 3 f(x) = g(x) = x 2 3 f(g(x)) = f(x 2) 3 f(g(x)) = x 2 Therefore we can write the following: Step 2 of 4 Next obtain mean . This is very similar as the previous case. We will put the value of in place of x in the function Hence, And 3 g(x) = x 2 f(x) =x g(f(x)) = g(x) 3 1/23 g(f(x)) = (x) 2=(x ) 2 Based on the rule (x ) = x ab we can write the following: g(f(x))=x 3/2 2 Therefore we have: 3/2 g ° = x 2