Question

If `f(x)=x^2-81` and `g(x)=(x-9)^(-1)(x+9)`, find `g(x)xxf(x)`.

Answer 1

For this case we have the following fusions:

$f (x) = x ^ 2-81\\g (x) = (x-9) ^ {- 1} * (x + 9)$

We can rewrite g (x) as:

1. $g (x) = \frac {(x + 9)} {(x-9)}$

According to the following power property:

$a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}$

Also:

If we factor f (x) we have:

$f (x) = (x + 9) (x-9)$

We must find:

$f (x) * g (x) = (x + 9) (x-9) * \frac {(x + 9)} {(x-9)}$

We simplify common terms in numerator and denominator:

$f (x) * g (x) = (x + 9) ^ 2$

ANswer:

$f (x) * g (x) = (x + 9) ^ 2$

Answer 2

Answer:

$g ( x ) * f ( x ) = ( x + 9 ) ^ 2$

Step-by-step explanation:

We are given the following two functions and we are to find $g(x) * f(x)$:

$f(x)=x2-81$

$g(x)=(x - 9)^{-1} ( x + 9)$

$g(x)*f(x)=x^{-81} * \frac{x+9}{x-9}$

$g ( x ) * f ( x ) =\frac{(x+9)(x-9)(x+9)}{x-9}$

$g ( x ) * f ( x ) = ( x + 9 ) ( x + 9 )$

$g ( x ) * f ( x ) =( x + 9 ) ^ 2$