Determine whether (f  g)(x) = x and whether (g  f)(x) = x.
-$f ( x ) = x ^ { 2 } + 3 , g ( x ) = \sqrt { x } - 3$
A) Yes, no
B) No, yes
C) Yes, yes
D) No, no

Question

Quizplus · Accepted Answer

To determine if these compositions equal x, we need to compute both (f ue048 g)(x) and (g ue048 f)(x).First, compute (f ue048 g)(x) = f(g(x)):$$f(g(x)) = f(\sqrt{x} - 3) = (\sqrt{x} - 3)^2 + 3 = x - 6\sqrt{x} + 9 + 3 = x - 6\sqrt{x} + 12$$This does not simplify to x, so the first part is "no".Next, compute (g ue048 f)(x) = g(f(x)):$$g(f(x)) = g(x^2 + 3) = \sqrt{x^2 + 3} - 3$$This also does not simplify to x, so the second part is "no".Therefore, both compositions do not equal x, making the correct answer D) No, no.

Determine Whether (F  G)(x) = X and Whether (G f(x)=x2+3,g(x)=x−3f ( x ) = x ^ { 2 } + 3 , g ( x ) = \sqrt { x } - 3f(x)=x2+3,g(x)=x​−3

Determine Whether (F  G)(x) = X and Whether (G $f ( x ) = x ^ { 2 } + 3 , g ( x ) = \sqrt { x } - 3$