Domain and range of composite functions?

[CAH]

hey!
How do you work out the domain and range of fg(x), do you work out what range of g(x) will fit the domain of f(x)?

I have no clue.

Thanks

 

[DannyMoretz]

Hey CAH,
Sorry, but do you mean f(g(x)) or f(x) * g(x) ?

 

[jbriggs444]

°

How do you work out the domain and range of fg(x), do you work out what range of g(x) will fit the domain of f(x)?

Based on the thread title, by fg(x) you mean f(g(x)). So you are trying to work out the domain and range for the composition of f with g.

For the range, you would start with the range of the inner function -- g in this case. Figure out what outputs are possible from f when its inputs are in that range.

For the domain, you would start with the domain of the outer function -- f in this case. Figure out what inputs to g can produce outputs in that range.

 

[CAH]

for example:
f(x)=3e^(2x) domain:(-infinity, +infinity)
g(x)=ln(4x) domain:(0, +infinity)

how would i go about finding the domain and range of f(g(x))?

(thanks for the reply)

 

[HallsofIvy]

First, to be in the domain of f(g(x)), x must first be in the domain of g. Then it must be true that g(x), for that particular x, is in the domain of f. Here, the domain of f is all real numbers so the domain of f(g(x)) is just the domain of g. As for range, g(x) can give any real number but f of any number is positive so the range of f(g(x)) is the set of positive real numbers.