Question

Given functions F(x) = (x - 16)/(x^2 + 6x - 40) for x ≠ -10 and x ≠ 4, and g(x) = 1/(x + 10) for x ≠ -10. Find the value of g(F(7)).

a) -1/3
b) -3
c) 3
d) 1/3

Answer 1

After calculating F(7) and then substituting it into g(x), we find that g(F(7)) simplifies to a value near 1/10, which is not among the provided options, suggesting there may be an error in the question.

Step-by-step explanation:

The task is to find the value of g(F(7)). First, we calculate F(7) by substituting x = 7 into the function F(x) which is F(7) = (7 - 16) / (7^2 + 6(7) - 40). Simplifying this gives us F(7) = -9 / (49 + 42 - 40), which simplifies further to F(7) = -9 / 51 or -1 / 6. Then, we substitute -1 / 6 into g(x), giving us g(-1/6) which is 1 / (-1/6 + 10). This simplifies to 1 / (9 5/6) or 1 / (59/6). By inverting the fraction, we get 6 / 59. Finally, simplifying this fraction gives us the result, which is very close to 1/10, which isn't an option provided in the original question, indicating a potential error in the options listed.