Question

Simplify the function

Answer 1

1. 7

2. 3

3.
`(-\infty,\infty)`

4.
`(0,\infty)`

Explanation:

You are given the function
`f(x)=7(\sqrt[3]{54} )^x.`

1. The inital value can be obtained when x=0:

`f(0)=7(\sqrt[3]{54} )^0=7\cdot 1=7.`

2. The base of the function is
`\sqrt[3]{54}.` Since
`54=27\cdot 2,` then

`\sqrt[3]{54}=\sqrt[3]{27\cdot 2} =\sqrt[3]{27} \cdot \sqrt[3]{2}=3\cdot \sqrt[3]{2} .`

3. The domain of the exponentioa function is all real numbers.

4. The range of the function is
`f(x)>0` or
`(0,\infty).`