2 Answers

Luc Ebert · Answer 1 · 2020-01-05T20:29:18+0000

Hello!

The answer is:
$g(x)=-\sqrt[3]{x-1}$

Let's check the roots and the shown point in the graphic (2,-1)

First,

$0=-\sqrt[3]{x-1}\\\\0^(3)=(-\sqrt[3]{x-1})^(3)\\\\0=-(x-1)\\\\x=1$

then,

$g(0)=-\sqrt[3]{0-1}\\g(0)=-(-1)\\g(0)=1\\y=1$

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

(
$g(x)=-\sqrt[3]{x-1}$ )

Second,

Evaluating the function at (2,-1)

$y=-\sqrt[3]{x-1}\\-1=-\sqrt[3]{2-1}\\-1=-\sqrt[3]{1}\\-1=-(1)\\-1=-1$

-1=-1

It means that the function passes through the given point.

Hence,

The equation which represents g(x) is
$g(x)=-\sqrt[3]{x-1}$

Have a nice day!