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SAT Math 1.5 Algebra and Functions 218 Views


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SAT Math 1.5 Algebra and Functions. If f (x) = x 2 - 16 and g(x) = x 4 - 256, what is f of x divided by g of x?

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Transcript

00:02

Getting Shmoopy with it...

00:04

The question:

00:05

If f (x) = x2 - 16 and g(x) = x4 - 256, what is f of x divided by g of x?

00:16

And here are the potential answers...

00:21

Let's first put in the functions f of x divided by g of x.

00:26

Then we plug in the given functions here, so that's:

00:30

x squared minus 16 divided by x to the fourth minus 256.

00:35

The numerator and denominator both look like they're begging to be factored.

00:42

But let's start with the denominator ….because it has the larger exponent.

00:45

Hmmm, what does this ugly number factor into?

00:49

Well it kind of looks like a difference of two squares..

00:51

x to the fourth is a square of x squared...

00:55

And 256 is a perfect square of 16...

00:58

So we have x squared minus 16 times x squared plus 16.

01:02

Hey! The numerator just so happens to have (x2 - 16) as well.

01:07

Instead of factoring that equation even further, we can cancel both the numerator

01:12

and one of the factors in the denominator and arrive at 1 over x squared plus 16.

01:17

Answer's (A).

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