Determine whether (f(g(x)) $$( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x$$
-$f ( x ) = x ^ { 2 } + 5 , g ( x ) = \sqrt { x } - 5$
A) No, yes
B) Yes, yes
C) Yes, no
D) No, no

Question

Quizplus · Accepted Answer

For $f(g(x))$, substituting $g(x) = \sqrt{x} - 5$ into $f(x) = x^2 + 5$, we get $f(g(x)) = (\sqrt{x} - 5)^2 + 5 = x - 10\sqrt{x} + 25 + 5 = x - 10\sqrt{x} + 30$, which is not equal to $x$. For $g(f(x))$, substituting $f(x) = x^2 + 5$ into $g(x) = \sqrt{x} - 5$, we get $g(f(x)) = \sqrt{x^2 + 5} - 5$, which is not equal to $x$.

Determine Whether (F(g(x)) (f(g(x))=x and whether (g(f(x))=x( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x(f(g(x))=x and whether (g(f(x))=x

Determine Whether (F(g(x)) $( f ( g ( x ) ) = x \text { and whether } ( g ( f ( x ) ) = x$