Hello!
The answer is: [tex]g(x)=-\sqrt[3]{x-1}[/tex]
Why?
Let's check the roots and the shown point in the graphic (2,-1)
First,
[tex]0=-\sqrt[3]{x-1}\\\\0^{3}=(-\sqrt[3]{x-1})^{3}\\\\0=-(x-1)\\\\x=1[/tex]
then,
[tex]g(0)=-\sqrt[3]{0-1}\\g(0)=-(-1)\\g(0)=1\\y=1[/tex]
So, we know that the function intercepts the axis at (1,0) and (0,1), meaning that the function match with the last given option
([tex]g(x)=-\sqrt[3]{x-1}[/tex])
Second,
Evaluating the function at (2,-1)
[tex]y=-\sqrt[3]{x-1}\\-1=-\sqrt[3]{2-1}\\-1=-\sqrt[3]{1}\\-1=-(1)\\-1=-1[/tex]
-1=-1
It means that the function passes through the given point.
Hence,
The equation which represents g(x) is [tex]g(x)=-\sqrt[3]{x-1}[/tex]
Have a nice day!
