Question

Can you please help me on my review?

Answer 1

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 ...

  $g(x)=\sqrt[3]{-(x-7)}\\\\g(x)=-\sqrt[3]{x-7}$