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# Algebra and Functions Help watch

1. (Original post by emx_eco)
ooooooh therefore the domain is x > 3. I get it now thank you!!

Do you think you could help me with part b) -

f(x) = e^(2x) + 3 where x is any real number
g(x) = ln(x-1) where x is any real number and x > 1

Find fg(x) and state its range
Have you made a start?
2. (Original post by _gcx)
Have you made a start?
so at the moment I have:

fg(x) = eln(x-1)^2+ 3
3. (Original post by emx_eco)
so at the moment I have:

fg(x) = eln(x-1)^2+ 3
Not quite.

You should have have . You can write this as . Do you know what to do from there?

(unless you meant or , then you're fine)
4. (Original post by _gcx)
Not quite.

You should have have . You can write this as . Do you know what to do from there?

(unless you meant , then you're fine)
how can you write it in that format? what is the rule?
5. (Original post by emx_eco)
how can you write it in that format? what is the rule?
. You also have .
6. (Original post by _gcx)
. You also have .
oh okay I understand that now. So whats comes next?
7. (Original post by emx_eco)
oh okay I understand that now. So whats comes next?
You should be fine that . Are you familiar with how to proceed?
8. (Original post by _gcx)
You should be fine that . Are you familiar with how to proceed?
how do these two things equal each other?
9. (Original post by emx_eco)
how do these two things equal each other?
10. (Original post by _gcx)
how come the e cancels out? (sorry for so many questions!)
11. (Original post by _gcx)
Does it??
12. (Original post by Ano9901whichone)
Does it??
yes... it is given in the question that . Please don't confuse the OP, even if your comment was in jest.
13. (Original post by emx_eco)
how come the e cancels out? (sorry for so many questions!)
because is the inverse of A property of inverse functions is that .
14. (Original post by _gcx)
because is the inverse of A property of inverse functions is that .
ohhhhh! So now that you have (x-1)^2 +3 you just sketch it with the minimum point (1,3) meaning the range is f(x) > 1? (thats meant to be the bigger than or equal to sign with the line underneath)
15. (Original post by emx_eco)
ohhhhh! So now that you have (x-1)^2 +3 you just sketch it with the minimum point (1,3) meaning the range is f(x) > 1? (thats meant to be the bigger than or equal to sign with the line underneath)
Close, that's the domain. (, remember that is undefined) The range is . Can you see why?
16. (Original post by _gcx)
Close, that's the domain. (, remember that is undefined) The range is . Can you see why?
oh wait yh, my mistake! Thanks so much for all your help xxx

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