Please Help with Pre-Calc Questions anybody please...?
For each of the following functions, identify any restrictions on its domain.
5. F(x) = cubroot of (x-2) +3
6. F(x)=log(x-5)+1
7.e^(x+4)+7
Is there any value of x that would cause this function to be undefined?
If there are restrictions on the domain, explain those restrictions.
If there are no restrictions, explain why that is.

- anonymous

- chestercat

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- freckles

well can you do cuberoot of any real number?
for example do you know the cuberoot(-1)=?
or the cuberoot(0)=?
or the cuberoot(1)=?

- anonymous

wouldn't it be -1?

- freckles

yes
so you can do cuberoot(-1)=-1
so you can do cuberoot of negative numbers or even 0 or positive numbers right?

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- freckles

The cuberoot function is defined everywhere.

- freckles

what about log
can you do log(0) or log(-1)?

- anonymous

right

- anonymous

it would be undef?

- freckles

so you know you do log(positive) only

- freckles

so you will have restrictions for the log function you have above

- anonymous

yes

- freckles

you want x-5 to be positive

- freckles

therefore you want x-5 greater than 0
so just solve x-5>0

- anonymous

so for the firs question i just say that it is undef at log(-1) and log(0)?

- freckles

well it is undefined when the inside is negative or zero
so if you are looking where it is undefined instead of define
just negate x-5>0
and you have x-5<=0

- anonymous

? how would i answer the first question?im confused

- freckles

I thought we already said yes to that question because you cannot do log(negative or zero number)

- freckles

we can do log(positive number)
x-5 is positive when it is greater than 0
so you can find x such that x-5>0 by solving the inequality

- anonymous

srry i thought your most recent post was about the first question..

- freckles

I'm confused.

- freckles

I thought the first question is it undefined anywhere

- anonymous

just continue i understand now

- anonymous

hello?

- freckles

hi

- freckles

do you have any questions?

- anonymous

there u are

- anonymous

yes can u help me with the rest of them?

- freckles

Do you know anything about e^x?

- freckles

Do you know of any restrictions ?

- freckles

for example does
e^(-7)
or e^(0)
or e^(8) exist?

- freckles

can you raise positive numbers to a negative,0, or positive power?

- anonymous

srry i type slow

- anonymous

yes it comes out a decimal

- freckles

ok e^x exists everywhere

- freckles

you can also look at a visual and see this too

- anonymous

ok

- freckles

so only one of the functions you listed has restrictions (or some place where it is not defined) over the real numbers

- anonymous

ok thank u i appreciate it

- freckles

so you did understand cuberoot and exponential functions exist everywhere over the real numbers and has domain all real numbers
but log functions do have restrictions over the real number because you can only do log(positive numbers)

- anonymous

yes

- anonymous

now i do thank u

- freckles

np

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