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Sagot :
The question provides two functions:
[tex]\begin{gathered} f(n)=4n+7 \\ g(n)=2n+3 \end{gathered}[/tex]We are then told to find (g - f)(n).
Using the Operation of functions we can solve this problem.
[tex](g-f)(n)=g(n)-f(n)[/tex]Since we know what g(n) and f(n) are, we can find (g - f)(n).
This is done below:
[tex]\begin{gathered} (g-f)(n)=g(n)-f(n) \\ g(n)=2n+3 \\ f(n)=4n+7 \\ \\ \therefore(g-f)(n)=g(n)-f(n)=(2n+3)-(4n+7) \\ (g-f)(n)=2n+3-4n-7 \\ \\ \text{Collect like terms} \\ \\ (g-f)(n)=2n-4n-7+3 \\ \therefore(g-f)(n)=-2n-4 \\ \\ \end{gathered}[/tex]Therefore, the final answer is:
-2n - 4
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