Answer:
Step-by-step explanation:
This is function composition. We will take the g function and plug it into the f function wherever we see an x. That will look like this when it's done but before it's simplified:
and that can be simplified down to
The domain of this function will be all real numbers EXCEPT for the one(s) that cause the denominator to become undefined. Set the denominator equal to 0 and solve for x:
5x - 4 = 0 so
5x = 4 and
x = 4/5
In other words, D = {x | x ≠ 4/5}
Answer:
You gave the explicit form.
Step-by-step explanation:
You gave the explicit form.
The recursive form is giving you a term in terms of previous terms of the sequence.
So the recursive form of a geometric sequence is and they also give a term of the sequence; like first term is such and such number. All this says is to get a term in the sequence you just multiply previous term by the common ratio.
r is the common ratio and can found by choosing a term and dividing by the term that is right before it.
So here r=-3 since all of these say that it does:
-54/18
18/-6
-6/2
If these quotients didn't match, then it wouldn't be geometric.
Anyways the recursive form for this geometric sequence is