SOLUTION: f(x)=x^2+1 and g(x)=x^2−1. Find (f∘f)(x), (f∘g)(x), and (g∘f)(x).

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Question 1167053: f(x)=x^2+1 and g(x)=x^2−1. Find (f∘f)(x), (f∘g)(x), and (g∘f)(x).
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
f(x)=x2+1 and g(x)=x2−1.
Find (f∘f)(x), (f∘g)(x), and (g∘f)(x)
(f∘f)(x) means to plug the right side of f(x) for x into the right side of f(x).

Plugging the right side of f(x), which is (x2+1), for x into the
right side of f(x) gives:

 (f∘f)(x) = (x2+1)2+1

-----------------------------------------------

(f∘g)(x) means to plug the right side of g(x) for x into the right side of
f(x).

Plugging the right side of g(x), which is (x2-1), for x, into the
right side of f(x) gives:

 (f∘g)(x) = (x2-1)2+1

-----------------------------------------------

(g∘f)(x)  means to plug the right side of f(x) for x into the right side of g(x).

Plugging the right side of f(x), which is (x2+1) for x, in the right
side of g(x) gives:

 (g∘f)(x) = (x2+1)2-1

------------------------------------------------

Edwin
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