Question

PLEASE HELP ME WITH THIS PROBLEM
If f(x)=lnx,g(x)=e^5x, and h(x)=x^8, find the following.
(a) (f(g(x)) and what is the domain
(b) g(f(x)) and what is the domain
(c)(f(g(7))
(d)(f(h(x)) and what is the domain
(e) (f(h(e))

Answer 1

do you mean f(x) = lnx

Answer 2

yes! thank you for catching that!

Answer 3

f(x) = ln(x)

f(g(x)) = ln(g(x))

f(g(x)) = ln(e^(5x))

f(g(x)) = 5x*ln(e)

f(g(x)) = 5x

Answer 4

the domain is the set of all real numbers since you can plug in any real number you want to get some real number as an output

Answer 5

okay would it be the same for b? just change the number?

Answer 6

well you'll get the same result, just take a different path

Answer 7

g(x) = e^(5x)

g(f(x)) = e^(5*f(x))

g(f(x)) = e^(5*ln(x))

g(f(x)) = e^(ln(x^5))

g(f(x)) = x^5

actually you won't get the same result, i jumped the gun a bit there...but the domain is still the set of all real numbers

Answer 8

okay understand now.

Answer 9

you're basically doing this for every part a) through e)

Answer 10

would the next be equal to 35

Answer 11

it would

Answer 12

what about part d

Answer 13

I got to the point where it is 8lnx not sure where to go from there

Answer 14

that's as far as you can go

Answer 15

so

f(h(x)) = 8*ln(x)

where the domain is x > 0

Answer 16

oh! lol okay so then e will be just 8

Answer 17

yep

Answer 18

thank you very much!

Answer 19

you're welcome

Answer 20

is there a chance you can help me with just two more problems?

Answer 21

sure

Answer 22

that sounds doable

Answer 23

Thank you SOoo much should I post it here or a new one?

Answer 24

either way works