21-30. Composite functions and notation Let \(f(x)=x^2-4,\ g(x)=x^3,\) and F(x) = 1/(x - 3). Simplify or evaluate the following expressions.

F(g(w))

Step by step solution Step 1 of 1 2 3 Consider three different functions f(x)=x -4, (x)=x and F(x)= 1/(x-3). If we want to find the value of function f(x) for x =g(w) we must use the function g(w) in the relation for the fun ction F(x).This is very easy, just follow the next steps: f(x) = x 4 i nc (w)=w then we have: 2 f(g(w)) = (g(w)) 4 = (w ) 4 a b ab Based on the rule (x ) = x we can write the following: f(g(w)) = w 46 6 So the final value of the function f(g(w))is w 4.