We have to find the equation of F(x) when it is shifted 5 units to the left.
When translating a function in the horizontal axis, the change in the function happens in the argument of the function.
In this case, we can select a known point of F(x) = 1/x.
We can pick x = 0, where we know that F(x) has its only discontinuity.
Then, for G(x), the translated function, this discontinuity has to be translated 5 units to the left. This means that the discontinity happens at x = -5.
Then, we can write G(x) as:
[tex]G(x)=F(x+5)=\frac{1}{x+5}[/tex]
Answer: G(x) = 1/(x+5) [Option D]
