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GRAPHS AND FUNCTIONSDetermining whether two functions are inverses of each otherFor each pair of functions fand g below, find f(g (x)) and g (f(x))Then, determine whether fand 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.)1(b) f(x) = x - 3(a) f(x)x 04x?X1g (x)x - 3g (x)x 04xf(g (x)f(g (x)) =g (r(x)) =g (f(x))=Ofand gOfand g are inverses of each otherare inverses of each other|Ofand g are not inverses of each otherfand gare not inverses of each other

Question

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GRAPHS AND FUNCTIONS
Determining whether two functions are inverses of each other
For each pair of functions fand g below, find f(g (x)) and g (f(x))
Then, determine whether fand 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.)
1
(b) f(x) = x - 3
(a) f(x)
x 0
4x
?
X
1
g (x)x - 3
g (x)
x 0
4x
f(g (x)
f(g (x)) =
g (r(x)) =
g (f(x))=
Ofand g
Ofand g are inverses of each other
are inverses of each other
|Ofand g are not inverses of each other
fand gare not inverses of each other
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GRAPHS AND FUNCTIONS Determining whether two functions are inverses of each other For each pair of functions fand g below, find f(g (x)) and g (f(x)) Then, determine whether fand 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.) 1 (b) f(x) = x - 3 (a) f(x) x 0 4x ? X 1 g (x)x - 3 g (x) x 0 4x f(g (x) f(g (x)) = g (r(x)) = g (f(x))= Ofand g Ofand g are inverses of each other are inverses of each other |Ofand g are not inverses of each other fand gare not inverses of each other

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check_circleAnswer
Step 1

Answer(a): f(g(x))=

f(g(x))
4х
1
4х
1
1
х
=X
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f(g(x)) 4х 1 4х 1 1 х =X

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Step 2

Answer(a): g(f(x))= x

f and g are inverse functions of each other.

g(f (x))
4x
1
4x
1
X
=X
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g(f (x)) 4x 1 4x 1 X =X

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Step 3

Answer(b): f(g(x))= x-6...

(g(x))
=f (x-3)
(x-3)-3
=x-3-3
=x-6
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(g(x)) =f (x-3) (x-3)-3 =x-3-3 =x-6

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