Question

What is the domain of the function f(x) =sin-1[log2(x/2)]

Answer 1

Given: The term f(x) =sin^-1 [log(base 2) (x/2) ]

To find: What is the domain of the given function?

Solution:

• Now we have given the term: f(x) =sin^-1  [log(base 2) (x/2) ]

• Now for domain, we have:

                  -1 ≤ [log(base 2) (x/2) ] ≤ 1

                  -1/2 ≤ x/2 ≤ 2

                  -2/2 ≤ x ≤ 2(2)

                  -1 ≤ x ≤ 4

                  Domain ∈ [-1 , 4]

Answer:

            So the domain is [-1 , 4].

Answer 2

Answer:

Given: The term f(x) =sin^-1 [log(base 2) (x/2) ]

To find: What is the domain of the given function?

Solution:

Now we have given the term: f(x) =sin^-1  [log(base 2) (x/2) ]

Now for domain, we have:

                  -1 ≤ [log(base 2) (x/2) ] ≤ 1

                  -1/2 ≤ x/2 ≤ 2

                  -2/2 ≤ x ≤ 2(2)

                  -1 ≤ x ≤ 4

                  Domain ∈ [-1 , 4]

Answer:

            So the domain is [-1 , 4].

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