Respuesta :

alinakincsem

Answer:

[tex] g ( x ) * f ( x ) = ( x + 9 ) ^ 2 [/tex]

Step-by-step explanation:

We are given the following two functions and we are to find [tex]g(x) * f(x)[/tex]:

[tex]f(x)=x2-81[/tex]

[tex]g(x)=(x - 9)^{-1} ( x + 9)[/tex]

[tex]g(x)*f(x)=x^{-81} * \frac{x+9}{x-9}[/tex]

[tex]g ( x ) * f ( x ) =\frac{(x+9)(x-9)(x+9)}{x-9}[/tex]

[tex] g ( x ) * f ( x ) = ( x + 9 ) ( x + 9 ) [/tex]

[tex]  g ( x ) * f ( x ) =( x + 9 ) ^ 2 [/tex]

carlosego

For this case we have the following fusions:

[tex]f (x) = x ^ 2-81\\g (x) = (x-9) ^ {- 1} * (x + 9)[/tex]

We can rewrite g (x) as:

  1. [tex]g (x) = \frac {(x + 9)} {(x-9)}[/tex]

According to the following power property:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Also:

If we factor f (x) we have:

[tex]f (x) = (x + 9) (x-9)[/tex]

We must find:

[tex]f (x) * g (x) = (x + 9) (x-9) * \frac {(x + 9)} {(x-9)}[/tex]

We simplify common terms in numerator and denominator:

[tex]f (x) * g (x) = (x + 9) ^ 2[/tex]

ANswer:

[tex]f (x) * g (x) = (x + 9) ^ 2[/tex]

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