To find: The domain and the range of the function.
The domain of the function h(x) is .
The range of the function h(x) is .
The function .
The domain is the set of all input values of the function for which the function is real and defined.
The function is defined when .
Hence, the function is defined for the numbers .
Therefore, the domain of the function is .
The range is the set of all output values of the function. So, find the output for the input values lies in the interval .
Observe that as x gets closer to −6, but greater than −6, the value of h(x) approaches −∞.
Similarly, as x gets closer to −6, but greater than −6, the value of h(x) approaches ∞.
Thus, it can be concluded that the range of the function is .
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