Question

Evaulate f(x)= 2x^2+3x+5 at f(x^2+x)

Answer 1

SO the domain..... JUst need a refresher on how to determine the domain?

Answer 2

start by trying to find any x-values where the function is undefined
the result from this calculation is


2 x^4 + 4 x^3 + 5 x^2 + 3 x + 5

are there any x-values that make this undefined?

Answer 3

0?

Answer 4

well we would just end up with zero

Answer 5

hm, not quite, if we plug in x = 0 we get 5 which is fine

there aren't really any x-values that make this undefined so we say the domain is all real values

Answer 6

not even neg

Answer 7

other ways to express this:

(-infinity, infinity) or capital R with an extra bar (trying to find this)

Answer 8

there we go

Answer 9

ah, yes

since you have a square root the expression under the square root sign must be 0 or more

so x^2 - 4 >= 0

x^2 >= 4

this is true for all values greater than/equal to 2 or less than/equal to -2

Answer 10

I just need a clear answer lol not saying your wrong. I have my midterm in calc tomorrow so am just refreshing everything

Answer 11

the website is technically incorrect as it should be "all real values except [-2,2]" with closed brackets not parentheses

Answer 12

so where are you getting the 2,-2 from

Answer 13

is it because of x^2 is four and the square root is 2?

Answer 14

so the expression under the root sign is "x^2-4"

we know that the expression under a root sign has to be 0 or more

so we set up the inequality

x^2 - 4 >=0

adding 4 to both sides

x^2 >= 4

taking the square root of both sides tells us that x must be 2 or more, OR -2 or less

Answer 15

so instead of saying "what must x be" we can specify "what CAN'T x be" and since we can't have x-values between -2 and 2 we say "all real values EXCEPT [-2,2]"

Answer 16

or, you could also say

(-infinity,-2] to [2,infinity) as an equally valid answer

Answer 17

for the multiplication law of exponents ...ot os (x^a)^b=x^ab

Answer 18

Do you leave it as x^ab or is it really x^a*b?

Answer 19

x^ab and x^a*b are technically the same thing

the second one makes it more clear that you multiply a*b first before taking the exponent

Answer 20

oh okay so you do multiply it

Answer 21

the exponents?

Answer 22

multiply the exponents, yes

Answer 23

okAY

Answer 24

so (x^2)^3 = x^6

Answer 25

and what if it is the addition property like x^6x^7= it would obviously be x^13 but if the bases are not the same like x^6y^7?

Answer 26

it would be like an error problem right?

Answer 27

x^6y^7 cannot be simplified further and must be left as is

Answer 28

could you show me an example of distributive law over multiplication

Answer 29

FOIL is an example

but for something simple

A(B+C) = A*B + A*C

Answer 30

Got it