Answer:
1. 7
2. 3
3. [tex](-\infty,\infty)[/tex]
4. [tex](0,\infty)[/tex]
Step-by-step explanation:
You are given the function [tex]f(x)=7(\sqrt[3]{54} )^x.[/tex]
1. The inital value can be obtained when x=0:
[tex]f(0)=7(\sqrt[3]{54} )^0=7\cdot 1=7.[/tex]
2. The base of the function is [tex]\sqrt[3]{54}.[/tex] Since [tex]54=27\cdot 2,[/tex] then
[tex]\sqrt[3]{54}=\sqrt[3]{27\cdot 2} =\sqrt[3]{27} \cdot \sqrt[3]{2}=3\cdot \sqrt[3]{2} .[/tex]
3. The domain of the exponentioa function is all real numbers.
4. The range of the function is [tex]f(x)>0[/tex] or [tex](0,\infty).[/tex]
