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

Step by step solution Step 1 of 1 Consider three different functions f(x)=x -4, (x)=x and F(x)= 1/(x-3). If we want to find the value of func tion (x) for =F(x) we must use the function F (x) instead x in the relation for the fun ction F (x).This is very easy, just follow the next steps: F(x) = x3 1 F(F(x)) = F(x)3 1 = 13 x3 Let’s simplify the previous relation: F(F(x)) = 1 x33 1 = x3 3x33) 1 = 13(x3) x3 = 1 1x3+9 1 = 103x x3 = x3 103x x3 So the final valu e of the function F (F(x)) is 103x .