The value of g(f(-7)) is 63/55 and this can be determined by using the given data and the function properties.
Given :
- \(\rm g(x) = \dfrac{x+8}{x}\)
First, determine the value of f(-7).
\(\rm f(-7) = (-7)^2+6\)
f(-7) = 49 + 6
f(-7) = 55
Now, the expression of g(f(x)) is given by:
\(\rm g(f(x)) = \dfrac{x^2+6+8}{x^2+6}\)
\(\rm g(f(x)) = \dfrac{x^2+14}{x^2+6}\)
Now, substitute the value of (x = -7) in the above expression.
\(\rm g(f(x)) = \dfrac{(-7)^2+14}{(-7)^2+6}\)
\(\rm g(f(x)) = \dfrac{49+14}{49+6}\)
\(\rm g(f(x)) = \dfrac{63}{55}\)
The value of g(f(-7)) is 63/55 and this can be determined by using the given data and the function properties. Therefore, the correct option is d).
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https://brainly.com/question/21114745
