198k views
3 votes
Find and simplify the function (gf)(x) given that f(x)=x-1 and g(x)=x²-1.

User Emeeus
by
8.3k points

1 Answer

4 votes

Final answer:

To simplify the function (gf)(x), substitute f(x) into g(x), resulting in g(f(x)) = (x-1)² - 1. When expanded and simplified, it becomes (gf)(x) = x² - 2x.

Step-by-step explanation:

To find and simplify the function (gf)(x), where f(x) = x - 1 and g(x) = x² - 1, we need to perform the composition of the two functions; that is, we substitute f(x) into every x in g(x).

Firstly, let's do the substitution to find (gf)(x):

g(f(x)) = g(x - 1) = (x - 1)² - 1

Now, let's simplify the expression:

(x - 1)² - 1 = (x² - 2x + 1) - 1

Simplifying further gives us:

x² - 2x

So the simplified form of (gf)(x) is x² - 2x.

User Aleskva
by
9.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories