Question

For each pair of functions ( f ) and ( g ) below, find ( f(g(x)) ) and ( g(f(x)) ). Then, determine whether ( f ) and ( g ) are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all ( x ) in the domain of the composition. You do not have to indicate the domain.) (a) ( f(x)=x+2 ) [ egin{array}{l} g(x)=x-2 \ f(g(x))=square \ g(f(x))=square end{array} ] ( f ) and ( g ) are inverses of each other ( f ) and ( g ) are not inverses of each other (b) [ egin{array}{l} f(x)=frac{1}{6 x}, x eq 0 \ g(x)=-frac{1}{6 x}, x eq 0 \ f(g(x))=square \ g(f(x))=square end{array} ] ( f ) and ( g ) are inverses of each other ( f ) and ( g ) are not inverses of each other

          For each pair of functions ( f ) and ( g ) below, find ( f(g(x)) ) and ( g(f(x)) ).
Then, determine whether ( f ) and ( g ) are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all ( x ) in the domain of the composition. You do not have to indicate the domain.)
(a) ( f(x)=x+2 )
[
egin{array}{l}
g(x)=x-2 \
f(g(x))=square \
g(f(x))=square
end{array}
]
( f ) and ( g ) are inverses of each other
( f ) and ( g ) are not inverses of each other
(b)
[
egin{array}{l}
f(x)=frac{1}{6 x}, x 
eq 0 \
g(x)=-frac{1}{6 x}, x 
eq 0 \
f(g(x))=square \
g(f(x))=square
end{array}
]
( f ) and ( g ) are inverses of each other
( f ) and ( g ) are not inverses of each other

$For each pair of functions ( f ) and ( g ) below, find ( f(g(x)) ) and ( g(f(x)) ). Then, determine whether ( f ) and ( g ) are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all ( x ) in the domain of the composition. You do not have to indicate the domain.) (a) ( f(x)=x+2 ) [ eginarrayl g(x)=x-2 f(g(x))=square g(f(x))=square endarray ] ( f ) and ( g ) are inverses of each other ( f ) and ( g ) are not inverses of each other (b) [ eginarrayl f(x)=frac16 x, x eq 0 g(x)=-frac16 x, x eq 0 f(g(x))=square g(f(x))=square endarray ] ( f ) and ( g ) are inverses of each other ( f ) and ( g ) are not inverses of each other$

Added by Partyka F.

Question

Please give Ace some feedback