g(n-7) is evaluated to be [tex]g(n-7)= \frac{n^2 - 14n + 43}{7n - 49}[/tex].
How to find the value of a function when the variable is given?
We can find the value of a function when the value of the variable is given by, substituting the value of the variable throughout the entire function and then simplifying it.
We can find the value of g(n-7) as shown below:
It is given that:
[tex]g(x) = \frac{x^2-6}{7x}[/tex]
We have to find the value of g(n-7).
We can substitute n-7 in the place of x in the equation of the function.
This can be done as shown below:
[tex]g(n-7)= \frac{(n-7)^2 - 6}{7(n-7)} \\g(n-7)= \frac{n^2 - 14n + 49 - 6}{7n - 49} \\g(n-7)= \frac{n^2 - 14n + 43}{7n - 49}[/tex]
Therefore, the value of g(n-7) is evaluated to be [tex]g(n-7)= \frac{n^2 - 14n + 43}{7n - 49}[/tex]. The correct answer is option A.
Learn more about evaluating functions here: https://brainly.com/question/2284360
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