Composition of functions ( f * g )( x ) = ?  ( g * f)( x ) = ? f( x ) = 1/( x + 3 ) ; g( x ) = x

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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f( x ) = 1/( x + 3 ) ; g( x ) = x

to find (f*g)(x) :

f*g(x) = f(g(x))

but f(x ) = 1/(x+3)

then by replacing x vaues with g(x):

f(g(x)) = 1/[g(x) + 3] = 1/x +3 = f(x)

for g*f(x)

g*f(x) = g(f(x))

but g(x) = x

replace x with f(x)

==> g(f(x)) = f(x) = 1/(x+3)

 

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neela | High School Teacher | (Level 3) Valedictorian

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f(Composition of functions ( f * g )( x ) = ?  ( g * f)( x ) = ?

f( x ) = 1/( x + 3 ) ; g( x ) = x.

Solution:

(f*g)(x) = f(g(x)) =  1/[g(x)+1] = 1/(x+1).

g(f(x)) : g(x) = x. Therfore g(f(x) = f(x) =1/(x+1)

 

 

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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In order to find the value of the composition of 2 functions, in our case f and g, we have to follow the steps:

Step 1: First, we have to find out the expression of the composition of the 2 functions:

(f*g)(x) = f(g(x))

To find f(g(x)) we have to substitute x by g(x) in the expression of f(x):

f(g(x)) = 1/(g(x) + 3)

Now, we'll substitute g(x) by it's expression:

1/(g(x) + 3) = 1/(x + 3)

f(g(x)) = 1/(x + 3) 

The next step is to calculate (g*f)(x).

g(f(x)) = f(x)

g(f(x)) = 1/( x + 3 )

Though the composition of 2 functions is not commutative, in this case the results of (f*g)(x) and (g*f)(x) are equal.

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