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Here are two functions:$$\begin{array}{ccc} f(x) & = & 3x^2-2x+ 4\\ g(x) & = & x^2-kx-6 \end{array}$$If $f(10) - g(10) = 10,$ what is the value of $k?$

 Dec 30, 2021
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Subtract functions: f(x) - g(x) = (3x^2 - 2x + 4) - (x^2 - kx - 6) = 2x^2 - (k + 2) x + 10

 

Plug in x = 10: f(10) - g(10) = 200 - 10(k + 2) + 10 = 10

 

Solve for k: k = 8

 Dec 30, 2021

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