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 Question from yzabelle, a student: find f+g f(x)=x^2-1 g(x)=square root of x+2

Hi,

I want to illustrate with some different functios.

Suppose

$h(x) = x^2 + 4 \mbox{ and } k(x) = x^3 + 2x^2 + 9$

then

$h(x) + k(x) = x^2 + 4 + x^3 + 2x^2 + 9 = x^3 + 3x^2 + 13.$

I just added the expressions and then simplified. Sometimes you can't make any simplification. For example if

$p(x) = \frac{1}{\sqrt{x + 4}} \mbox{ and } q(x) = x^2$

then

$p(x) + q(x) = \frac{1}{\sqrt{x + 4}} + x^{2}.$