If f(x) = 4x + 1 and g(x) = x2 – 2x + 1, what is f(g(x)) ?
Answer:
A) 4x2 – 8x + 5
B) x2 + 2x + 2
C) x2 – 2x + 2
D) 4x2 + 2x + 2

Question

jamesj · Answer

By definition of f(x),
$$ f(g(x)) = 4g(x) + 1 $$

Now use the definition of g(x) to evaluate that expression.

jamesj · Answer

Does what I've written so far make sense?

anonymous · Answer

you can also do the following (it is identical to what jamesj wrote, just looks different at the beginning)
first replace the general $$g(x)$$ by the specific one and write 
$$f(g(x))=f(x^2-2x+1)$$
then replace x in 
$$f(x)$$ by 
$$x^2-2x+1$$ to write 
$$4(x^2-2x+1)+1$$ and then a small bit of algebra.  notice it is exactly the same as what jamesj wrote,

anonymous · Answer

Thank you<33