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PSAT Math Diagnostic Videos 41 videos

PSAT 1.10 Math Diagnostic
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PSAT 1.10 Math Diagnostic. Which of the following is a factor of the expression?

PSAT 1.3 Math Diagnostic
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PSAT 1.3 Math Diagnostic. Which of the following most nearly represents the line of best fit?

PSAT 1.4 Math Diagnostic
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PSAT 1.4 Math Diagnostic. Which of the following conclusions is supported by the data in the graph?

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PSAT 1.38 Math Diagnostic 180 Views


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Description:

PSAT 1.38 Math Diagnostic. What is f(g(x))?

Language:
English Language

Transcript

00:00

Thank you We sneak and here's your shmoop du jour

00:05

Brought to you by fancy footwork Now that's a dancer

00:08

with some fancy feet Yeah All right If f of

00:12

x equals x squared minus four X minus three and

00:16

g f x equals two x plus five What is

00:19

f of g of x and hear the pencil answers

00:23

All right Difference in size Something here Okay well in

00:27

english this roughly translates to give this of that Is

00:32

this and that of this is that what is this

00:36

of that of that Make even less sense now doesn't

00:40

want let's stick with the math version so we can

00:42

solve this one with little substitution and just a bit

00:44

of fancy footwork We're told that g f x equals

00:47

two x plus five So when we're given this nasty

00:50

looking thing at the end we can plug in two

00:52

x plus five in place of g f x to

00:55

get f of the quantity Two Acts plus 5 well

00:59

from here we can plug in that same expression as

01:02

acts throughout the function F of x so f of

01:05

x equals x squared minus four X minus three and

01:09

that becomes f of the quantity Two x plus five

01:13

equals the quantity two x plus five squared minus four

01:18

times the quantity Two x plus five minus three it's

01:22

longer but simpler Go figure Now we can just multiply

01:25

everything out to simplify to x plus five square and

01:27

we'll have to use the distributive property to get four

01:31

x squared plus ten x plus ten x plus twenty

01:33

five The next part multiplies out negative eight x minus

01:37

twenty and finally there's that negative three on the end

01:41

reminding all like terms it looks like f of the

01:43

quantity two x plus five equals four x squared plus

01:45

twelve x plus two which is option d Well that

01:49

certainly was easier than we thought it would be that

01:51

what dance our way to the answer although i suppose

01:54

we could have completed it even faster if we've done 00:01:56.441 --> [endTime] the hustle

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