CPM Homework Help : PC Problem 1-41

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1-41.

Given $f(x)=x^2+2x$ and $g(x)=\sqrt{x+1}$ , evaluate each of the following composite function operations.

$g(x-2)$
Hint (a):
Replace every $x$ in the $g$ function with the expression $(x−2)$ . Then simplify.

$f(g(8))$
Hint (b):
Compute $g(8)$ first. Then replace every $x$ in the $f$ function with the value of $g(8)$ . Simplify.

$g(f(8))$
Hint (c):
Compute $f(8)$ first. Then replace every $x$ in the $g$ function with the value of $f(8)$ . Simplify.

$f(f(1))$
Hint (d):
Compute $f(1)$ first. Then replace every $x$ in the $f$ function with the value of $f(1)$ . Simplify.
Answer (d):
$f(3)=15$

$f(x+1)$
Step (e):
$f(x+1)=(x+1)^2+2(x+1)$

$g(f(x))$
Step (f):
$g(x^2+2x)=\sqrt{(x^2+2x)+1}$

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