Question

If f(x) = X – 6 and g(x) = 8x – 8,which statement is true?Click on the correct answer.-4 is in the domain of fºg.-4 is not in the domain of fºg.

Answer 1

If we want to apply composition g(x) on f(x), we have to assume x=8x-8 on f(x), that means:

$\begin{gathered} (f\circ g);f(8x-8)=\sqrt[]{(8x-8)-6} \\ f(g(x))=\sqrt[]{8x-8-6} \\ f(g(x))=\sqrt[]{8x-14} \end{gathered}$

Since it's a root function, we know that a root of a negative number doesn't exist, so -4 is not in the domain of f°g