SOLUTION: I want to check my answer to this problem: Consider the functions {{{f(x)= -x + 1}}} and {{{g(x)= -x^2 - 2x + 1}}} Then calculate {{{f(g(-3))}}} I set it up so that Step one

Algebra ->  Algebra  -> Functions -> SOLUTION: I want to check my answer to this problem: Consider the functions {{{f(x)= -x + 1}}} and {{{g(x)= -x^2 - 2x + 1}}} Then calculate {{{f(g(-3))}}} I set it up so that Step one      Log On

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Question 78552: I want to check my answer to this problem:
Consider the functions f%28x%29=+-x+%2B+1 and g%28x%29=+-x%5E2+-+2x+%2B+1
Then calculate f%28g%28-3%29%29
I set it up so that Step one: f+=+%28-x%5E2+-+2x+%2B1%29
Step two: f+=+-x%28-x%5E2+-2x+%2B+1%29+%2B+1
Is that correct? And should my answer be further simplified?
Thank you!!!!
Answer by tutor_paul(427) About Me  (Show Source):
You can put this solution on YOUR website!
Yes, you have set up the problem correctly. However, your Step 2
is more properly written as:
f%28g%28x%29%29=-x%28-x%5E2-2x%2B1%29%2B1 rather than f= ...
Now, you can just plug -3 in there for x and solve it.
Alternatively, you could find g(-3) first as below, then
plug that result into the f(x) equation:
First, calculate g%28-3%29:
g%28-3%29=-%28-3%29%5E2-2%2A%28-3%29%2B1
g%28-3%29=-9%2B6%2B1=-2
Now, plug this in to the f(x) equation. The "x" is now the
value you found for g(-3):
f%28g%28-3%29%29=1-%28-2%29
f%28g%28-3%29%29=3