Question 708367: Please help me to understand the process of answering this question. I would really like to master this concept! :) Thank you in advance.
Let f(x) = x + 5 and g(x) = x^2. Find (g ° f) (4)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
If  is a function defined by \ =\ x^2\ +\ 2x\ -\ 3) , then if you are asked to evaluate at some number, say, 2, which is to say evaluate ) , you simply have to substitute 2 for every instance of  in the definition of ) . That is: \ =\ (2)^2\ +\ 2(2)\ -\ 3\ = 5)
Likewise, \ =\ a^2\ +\ 2a\ -3) and \ =\ (\chi\ -\ \gamma)^2\ +\ 2(\chi\ -\ \gamma)\ -\ 3)
Doing a composite, ) is nothing more than evaluating the first function at the value of the second function, that is \right)\ =\ \left(\varphi(x)\right)^2\ +\ 2\left(\varphi(x)\right)\ -\ 3)
For your problem, you want  composite  , which is just of of , or \right)) .
\ =\ \left(g\circ f\right)(x)\ =\ g\left(f(x)\right)\ =\ \left(x\ +\ 5\right)^2)
Whether or not your instructor expects you to expand the squared binomial is a matter between s/he and you. In any case, you still need to evaluate )
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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