Compositions functions help?

Mathematics
Tutor: None Selected Time limit: 1 Day

I don't understand how to find the domain of a composition function...

f(x)=x^2-1 ; g(x)=x-2   What is the domain of f(g(x))?

Sep 2nd, 2015

Thank you for the opportunity to help you with your question!

domain is the values which x assumes. in your function f(x) it's domain is g(x):

f(g(x))=(x-2)^2-1.    Expand to get

x^2-4x+4-1= x^2-4x+3

solve for x:    x^2-4x=-3

x^2-4x+(4/2)^2=-3+(4/2)^2

(x-2)^2=1

Square root both sides to get: x-2=+ or -1

x=3 or 1

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 2nd, 2015

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