Question 1200649
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Answer: <font color=red size=4>58</font>


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Work Shown:


Method 1


Given functions are
{{{f(x) = x^2-6x+6}}}
{{{g(x) = 5x-4}}}


Add them and simplify
{{{(f+g)(x) = f(x)+g(x)}}}
{{{(f+g)(x) = (x^2-6x+6)+(5x-4)}}}
{{{(f+g)(x) = x^2-x+2}}}


Then plug in x = -7
{{{(f+g)(x) = x^2-x+2}}}
{{{(f+g)(-7) = (-7)^2-(-7)+2}}}
{{{(f+g)(-7) = 49+7+2}}}
{{{(f+g)(-7) = 56+2}}}
{{{(f+g)(-7) = 58}}}


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Method 2


Plug x = -7 into each function separately
{{{f(x) = x^2-6x+6}}}
{{{f(-7) = (-7)^2-6(-7)+6}}}
{{{f(-7) = 49+42+6}}}
{{{f(-7) = 91+6}}}
{{{f(-7) = 97}}}
and
{{{g(x) = 5x-4}}}
{{{g(-7) = 5(-7)-4}}}
{{{g(-7) = -35-4}}}
{{{g(-7) = -39}}}


Then add the two results
{{{(f+g)(-7) = f(-7)+g(-7)}}}
{{{(f+g)(-7) = 97+(-39)}}}
{{{(f+g)(-7) = 97-39}}}
{{{(f+g)(-7) = 58}}}


GeoGebra and Desmos are two great tools to quickly verify the answer.
Here's the link to the Desmos calculator results. Focus on the calculations in the left panel.
<a href = "https://www.desmos.com/calculator/oqagw26fxj">https://www.desmos.com/calculator/oqagw26fxj</a>


WolframAlpha is another verification tool.
<a href = "https://www.wolframalpha.com/input?i=f%28x%29%3Dx%5E2-6x%2B6%2Cg%28x%29%3D5x-4%2C+find+f%28-7%29%2Bg%28-7%29">https://www.wolframalpha.com/input?i=f%28x%29%3Dx%5E2-6x%2B6%2Cg%28x%29%3D5x-4%2C+find+f%28-7%29%2Bg%28-7%29</a>
I encourage you to explore other calculator options. 
Try not to let them do 100% of the work for you, but rather use them as a verification tool at the end.
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