If $$ f(x)=2 x^{2}+5 $$ and $$ g(x)=x^{2}-2 $$, find $$ (f-g)(x) $$

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To find $$(f - g)(x)$$, subtract $$g(x)$$ from $$f(x)$$:

$$
\begin{align*}
f(x) &= 2x^2 + 5 \
g(x) &= x^2 - 2 \
(f - g)(x) &= f(x) - g(x) \
&= (2x^2 + 5) - (x^2 - 2) \
&= 2x^2 + 5 - x^2 + 2 \
&= (2x^2 - x^2) + (5 + 2) \
&= x^2 + 7
\end{align*}
$$

**Answer:** $$(f - g)(x) = x^{2} + 7$$
$$(f - g)(x) = x^{2} + 7$$

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