Question

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Answer 1

Answer:

Domain of h(x) =(−∞,−1]∪[1,4]

Explanation:

Domain is all possible allowable x value inputs.

There are generally 2 cases that are not allowed in real functions :

Even square roots of negative numbers. (Not defined in R ).

Division by zero. (Not defined at all).

In this case there are no divisions (denominators) in h(x)

so we only consider case 1 of the square roots not allowed to be negative.

Doing so, it becomes clear that the first term is only negative if x>4 and the second term is only negative if x<1 .

So #

Hence the domain is {x∈R∣−∞<x≤1and1≤x≤4}

=(−∞,−1]∪[1,4] .

The graph makes it clear :

graph{sqrt(4-x)+sqrt(x^2-1) [-7.28, 10.5, -1.93, 6.95]}

Step-by-step explanation:

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