16 Let fx 1x2 1 and gx 1x 1 Compute f gx What is the dom

Let f(x) = (1/x^2) + 1 and g(x) = 1/(x - 1) Compute (f g)(x). (What is the domain of f g? Graph the function f g. Let M(x) = (2x - 1)/(x - 2). Compute M(x) and then Compute (M M)(x). Compute using the formula you obtained in part Check that your answer agrees with that obtained in part (a). Let F(x) = (x+ 1)^5,f(x) = x^5, and g(x) = x + 1 Which of the following is true for all x?

Solution

16. F(x) = (x +1)^5 ; f(x) = x^5 ; g(x) = x+1

To find (f o g)(x) , plug x = g(x) in f(x):

(f o g)(x) = (x+ 1)^5

Now we find (g o f)(x) , plug x = f(x) in g(x)

(g o f)(x) =( x+ 1)^5 +1

We can see that (f o g)(x) = (x+ 1)^5 = F(x) and not   (g o f)(x)