SAT Math 5.5 Algebra and Functions

SAT Math 5.5 Algebra and Functions

AlgebraFactoring
Algebra and FunctionsSolving Quadratic Equations by Factoring
FunctionsBuild new functions from existing functions
Quadratic Functions
LanguageEnglish Language
MathAlgebra
Passport to Advanced MathSolving quadratic equations
Product TypeSAT Math
SAT MathAlgebra and Functions

Transcript

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.