ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos

PSAT 1.38 Math Diagnostic 180 Views


Share It!


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

Related Videos

Secret Ingredients
391 Views

PSAT 1.3 Math Narrative Walkthrough. How many full packages of secret ingredient does the company have to buy to make one 50-gallon batch?

PSAT 1.1 Reading Diagnostic
1006 Views

PSAT 1.1 Reading Diagnostic. The main purpose of the first two paragraphs is to...what?

PSAT 2.2 Reading Diagnostic
379 Views

PSAT 2.2 Reading Diagnostic. What is the main rhetorical effect of this phrase in the second paragraph?

PSAT 1.3 Writing Diagnostic
282 Views

PSAT 1.3 Writing Diagnostic. To make the paragraph most logical, sentence 2 in the second paragraph should be placed...where?

PSAT 1.4 Writing Diagnostic
239 Views

PSAT 1.4 Writing Diagnostic. Which choice most effectively combines the two sentences in the underlined portion?