Final answer:
The function f(x) = (4x+7) / (11-x) has a domain of all real numbers except x=11, and its range is all real numbers.
Step-by-step explanation:
The function f(x) = (4x+7) / (11-x) has a domain and range that we can find through analysis. The domain is all real numbers except for where the denominator is zero, which is at x=11. To find the range, we must consider that this function is rational, and its range is all real numbers except possibly for a particular value that cannot be obtained by plugging in any x in the domain. Through analyzing the function, we can conclude that there is no horizontal asymptote that the function cannot reach. Therefore, the range of f(x) is also all real numbers, as there is no restriction on the values that f(x) can take from the formula alone.