Final answer:
The domain of (f∘g)(x) depends on the correct interpretation of the given functions f(x) and g(x). Assuming no typos, the domain is all real numbers except where g(x) would cause f(x) to be undefined. However, due to the presence of a typo, clarification is needed before the domain can be conclusively determined.
Step-by-step explanation:
The student is asking for the domain of the composite function (f∘g)(x) based on the given functions f(x)=1/5x and g(x)=1/8x−10. To find the domain of (f∘g)(x), we must determine the set of all x-values for which g(x) is defined and for which f(g(x)) is also defined. The domain of g(x) is all real numbers since it's a linear function with no restrictions. However, since f(x) has a denominator of 5x, its domain excludes x=0.
Hence, to find the domain of (f∘g)(x), we want to ensure that when we plug g(x) into f, we do not get a zero in the denominator. That means we need to find x such that 1/8x−10 != 0.
In this case, to solve for x, we would set the denominator equal to zero and solve for the value of x that would make it undefined. However, there is a typo in the given functions which makes it unclear if g(x) should in fact be 1/(8x) − 10 or (1/8)x − 10. If it's the former, the denominator cannot be zero, so x cannot be zero. If it's the latter, then x can be any real number since dividing by eight does not affect the domain.
Assuming a correction to (1/8)x − 10 for g(x), the domain of (f∘g)(x) would then be all real numbers except for the value that makes 1/8x − 10 equal to zero.
Since there appears to be confusion about the functions due to typos, it would be best to clarify the functions before proceeding with the analysis.