use the given function f to answer the following f(x)=-3x +lnx a.domain b. graph c. range & any asymptote of f  (continued next box)d. find f^-1 , the inverse of f e. fomain and range of f^-1...

use the given function f to answer the following

f(x)=-3x +lnx

a.domain b. graph c. range & any asymptote of f  (continued next box)

d. find f^-1 , the inverse of f

e. fomain and range of f^-1

f. graph f^-1

must show work

Asked on by mcelwee5

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mlehuzzah | Student, Graduate | (Level 1) Associate Educator

Posted on

I can only answer one of these questions per post, so i have edited the question. Feel free to repost the rest of these as separate questions.

The domain of a function is the set of x values that you can "legally plug in" to your function. So, for example, you can't take the square root of a negative number (unless you allow imaginary numbers). So you are only allowed to plug in positive numbers and zero into the square root function.

For ln x, the domain is positive numbers.

To see why: `y=ln x` means that `e^y=x`

e raised to any power (even a negative one) is a positive number.

Thus the only possible x values are positive.

Also, as long as I take a positive number, that number will have a natural log.

 

Now, I can take any x value and multiply it by -3, and add that to another term. So that part of the function doesn't limit the domain.

 

Thus the domain of the function is `(0, oo)`. That is, x can be any positive number (this doesn't include 0). 

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