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

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

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) * (x+9)/(x-9)`

`g ( x ) * f ( x ) =((x+9)(x-9)(x+9))/(x-9)`

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

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