Find $(f+g)(x)$ when $f(x)=5 x^{2}-3 x+1$ and $g(x)=2 x-6$

Step 1 ：Given functions are $f(x)=5 x^{2}-3 x+1$ and $g(x)=2 x-6$

Step 2 ：To find $(f+g)(x)$, we add the two functions together

Step 3 ：Add the corresponding terms of $f(x)$ and $g(x)$ together

Step 4 ：So, $(f+g)(x) = (5x^{2} - 3x + 1) + (2x - 6)$

Step 5 ：Simplify to get $(f+g)(x) = 5x^{2} - x - 5$

Step 6 ：Final Answer: \(\boxed{5x^{2} - x - 5}\)