Question

F(x) = \sqrt{x+8} ; g(x) = 8x - 12 Find f(g(x)).

Answer 1

$\mathbf{Task.} ~ f(x)=\sqrt{x+8}; ~ g(x)=8x-12. ~ \mathrm{Find} ~ f(g(x)).$

$f(g(x))=\sqrt{g(x)+8}=\sqrt{8x-12 + 8}=\sqrt{8x-4}=$

$=\sqrt{4(2x-1)}=2\sqrt{2x-1}.$

$Answer \colon f(g(x))=2\sqrt{2x-1}. ~ \blacktriangle$