Two function problems I have no clue how to start

[dirtydarsh]

For these two problems I have no clue how to start, but I'm gonna take a shot. Can you guys tell me if I'm on the right track or not and how to get on the right track?

1. If f(g(x)) = 8 + sqrt(4-3x) , state a possible function for both f(x) and g(x). Show all work leading to these two functions and show that your composition works.

I got f(x) = 8 + x
and
g(x) = sqrt(4-3x)

It seems too obvious.




2. Find ( f(x+h) - f(x) ) / h , for f(x) = 9x + 3

This one I have no clue on how to even start it, but would you substitute like this? :

( 9(x+h) + 3 - 9x - 3 ) / h
simplifies to
( 9x + 9h - 9x ) / h
simplfies to
9h/h
which simplifies to 9.

 

[dirtydarsh]

Help with 2 function problems

1. If f(g(x)) = 8 + sqrt(4-3x) , state a possible function for f(x) and g(x). Show that your composition works.

I think this is straightforward, but I feel like I am being tricked. For f(x), is it f(x) = 8 + x?
and for g(x), is it g(x) = sqrt(4-3x)?



2. Find (f(x-h)-f(x))/h , for f(x) = 9x + 3.
This also seems straightforward, but I'm not sure.
I simplified to (9(x-h) + 3 - 9x - 3)/h.
Then I simplified further to (9x-9h+3-9x-3)/h
which reduces to -9h/h
so I get -9?

 

[stapel]

1. If f(g(x)) = 8 + sqrt(4-3x) , state a possible function for f(x) and g(x). Show that your composition works.

I think this is straightforward, but I feel like I am being tricked. For f(x), is it f(x) = 8 + x?
and for g(x), is it g(x) = sqrt(4-3x)?

Those'll certainly work. I would expect that those are the functions they're expecting.

2. Find (f(x-h)-f(x))/h , for f(x) = 9x + 3.
This also seems straightforward, but I'm not sure.
I simplified to (9(x-h) + 3 - 9x - 3)/h.
Then I simplified further to (9x-9h+3-9x-3)/h
which reduces to -9h/h
so I get -9?

Yep!

P.S. Thank you for showing your steps and reasoning so nicely!