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If f(x) = x^2 - 81 and
g(x) = (x - 9)^-1 ( x + 9)

Find g(x) x f(x)

A. (x+9)^2
B. (x-9)^2
C. 2(x-9)
D. (x+9)(x-9)

I know how to set this up, I just don't understand how to do it with two parenthesis on the g(x) side and the -1 exponent is throwing me off, please provide a brief explanation including what the -1 does please.

Respuesta :

Since I'm on my phone, I can't write the solution in LaTeX, but I can try to explain the approach as best as I can.

We are given two separate functions, namely f(x) and g(x). Since f(x) is a difference of two squares (x^2 is a squared term and 81 is a squared term), we can rewrite it as (x + 9)(x - 9).

Now, this will help us when we multiply through by g(x). Let's discuss the solution to g(x). In exponent laws, any number to the power of a negative number will be reciprocated. That is, the function will turn into fractional notation.

Example: Rewrite x^-1 in positive index form.

Since the power is negative, we will need to reciprocate x^1 to get 1/(x^1).

Example: Rewrite 3x^-2 in positive index form.

Since the x term is only affected by the power, the 3 is left unchanged and stays on the numerator. Now, since the power is negative, we need to reciprocate x^2 to yield: 3/(x^2).

Using the same process, we can rewrite g(x) as being (x + 9)/(x - 9).

Now, we want f(x) * g(x) so that becomes:

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

(x - 9) cancels in the numerator and denominator to yield: (x + 9)^2

The answer is Option A (x+9)^2.

How to find g(x) x f(x) ?

When you multiply two functions together, you'll get a third function as the result, and that third function will be the product of the two original functions. For example, if you multiply f(x) and g(x), their product will be h(x)=f g(x), or h(x)=f(x)g(x).

We are given two separate functions, namely f(x) and g(x).

Since f(x) is a difference of two squares (x^2 is a squared term and 81 is a squared term), we can rewrite it as (x + 9)(x - 9).

If x is not equal to 9 then,

f(x) = x^2 - 81 and

g(x) = (x - 9)^-1 ( x + 9)= (x+9)/(x-9)

g(x) x f(x) =(x^2 - 81 ) x (x+9)/(x-9)

=> (x+9)(x-9) x (x+9)/(x-9)

=> (x+9)^2

Learn more about functions on : https://brainly.com/question/1530360

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