Question 297158: If f( x) = x^2 + 1 and g(x) = x-2 find [f degree g](x)
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! We need to find f(g(x)). There is no degree in the center. It is a tiny circle and it's read: "f of g compose x." The word compose is represented by the tiny circle here.
f(x) = x^2 + 1 and g(x) = x - 2
What does g(x) equal?
It equals x - 2, right?
Well, replace x in the other function (your f(x)) with x - 2 and simplify.
f(x - 2) = (x - 2)^2 + 1
Keep in mind that f(x - 2) means the same thing as f(g(x)).
Are you with me so far?
f(x - 2) = (x - 2)(x - 2) + 1
f(x - 2) = x^2 - 4x + 4 + 1
f(x - 2) = x^2 -4x + 5
So, f(g(x)) = x^2 - 4x + 5
Understand?
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