Question

What are the domain and range of f(x)=logx-5

Answer 1

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

Let's define some terms:

• Domain: the set of inputs in the function (in this case, it is x)
• Range: the set of all of the possible outputs (in this case, it is y)

Let's find the domain:

   For log(x),

           ⇒ the only inputs that are accepted are nonnegative and nonzero

               ⇒ therefore: Domain is (0, ∞)

Now let's find out the range:

    The biggest constraint of the output is log(x)

         ⇒ however log(x) has a range of (-∞,∞)

             ⇒ therefore the entire equation's range is

                      (-∞,∞)

Answer:

• Domain: (0,∞)
• Range: (-∞,∞)

Hope that helps!

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