Answer:
g(x) = -∛(x-7)
Step-by-step explanation:
Reflection in the y-axis changes the sign of x, so after this transformation, the function is ...
g(x) = f(-x)
Then, translation 7 units to the right replaces x by (x-7), so after both transformations, the function is ...
g(x) = f(-(x -7)) = f(-(x -7))
Using the given definition for f(x), we have ...
[tex]g(x)=\sqrt[3]{-(x-7)}\\\\g(x)=-\sqrt[3]{x-7}[/tex]
