- #1
nando94
- 33
- 0
I got a test and I am having trouble on functions. On the quiz we had this problem on composite functions.
given f(x) = 6/(3-x) and g(x) = 5/3x find the following
a. f of g
b. the domain of f of g
c. the range of f of g
My attempts
a. For a I got 6/3 - 5/3x = 18x/9x - 5 which was the right answer. No problems here. However I am stuck on b and c.
b.For b I got (-infinity, 0) (0, 5/9) (5/9, 3) (3,infinity). My teacher marked the 3's as wrong
and I don't know why. What I did was found the domain of f and g sperately and then excluded them from f of g. So I am kind of confused.
c. Right answer was (-infinity,0) (0,2) (2,infinity) For the range I kind of forgot how to find the range! But I found the inverse of f of g and then used the domain of the inverse since that's the range which was (-infinity,2)(2,infinity). Then I realized that since these were rational functions it was the horizontal asymptote but I am not sure if that's the right reason.
I really need help with this!
given f(x) = 6/(3-x) and g(x) = 5/3x find the following
a. f of g
b. the domain of f of g
c. the range of f of g
My attempts
a. For a I got 6/3 - 5/3x = 18x/9x - 5 which was the right answer. No problems here. However I am stuck on b and c.
b.For b I got (-infinity, 0) (0, 5/9) (5/9, 3) (3,infinity). My teacher marked the 3's as wrong
and I don't know why. What I did was found the domain of f and g sperately and then excluded them from f of g. So I am kind of confused.
c. Right answer was (-infinity,0) (0,2) (2,infinity) For the range I kind of forgot how to find the range! But I found the inverse of f of g and then used the domain of the inverse since that's the range which was (-infinity,2)(2,infinity). Then I realized that since these were rational functions it was the horizontal asymptote but I am not sure if that's the right reason.
I really need help with this!
Last edited: