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SAT Math 5.5 Algebra and Functions 208 Views


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SAT Math 5.5 Algebra and Functions

Language:
English Language

Transcript

00:02

You can't handle the Shmoop.

00:06

If  f of x equals x squared minus 100 over x squared plus 10x,

00:10

and f of x minus 5 equals 1/3, then x must be which of the following?

00:17

And here are the potential answers…

00:21

All right, so we’re trying to find out what x should be given two functions.

00:25

Well, the first function we’re given, x squared minus 100 over x squared plus 10x, can be factored.

00:32

X squared minus 100 looks a heck of a lot like the difference of two squares….

00:37

so the numerator becomes (x + 10) times (x - 10). And the denominator is x squared plus 10x…

00:42

which becomes x times (x + 10). There’s an x + 10 now in both the numerator

00:47

and denominator, so we can cancel out the x +10 in each place.

00:52

Our new equation looks like this: f of x equals x minus 10 over x.

01:00

We’re given that f of x minus 5 equals 1/3, so substituting x minus 5 into the first function,

01:10

we get f of x minus 5… equals x minus 5 minus 10…all over x minus 5… equals 1/3.

01:20

X minus 5 minus 10 simplifies to x minus 15. So x minus 15 over x minus 5 equals 1 over 3.

01:29

To eliminate the fractions on both sides,

01:31

we need to multiply both sides by (x - 5) and 3… to arrive at 3 times (x - 15) = x - 5.

01:40

We distribute the 3 so that 3x - 45 = x – 5…and solve.

01:47

And x equals 20. Our answer’s E.

01:50

And our messy functions are no more. Thank you, Mr. Clean.

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