Answer:
x=-3
Step-by-step explanation:
We need to see the number line before we can help you.. I'm sorry.
Step-by-step explanation:
There ya go my laddie. enjoy.
The inverse function is equal to f-1(x) = (x - 1)/3 and the value at f-1(6) is equal to 5/3.
To find the inverse, you need to switch the f(x) and x in the equation. Then you can solve for the new f(x). The result will be the inverse (f-1)
f(x) = 3x + 1 ----> Switch f(x) and x
x = 3f(x) + 1 ----> Subtract 1
x - 1 = 3f(x) ----> Divide by 3.
f-1(x) = (x - 1)/3
Now that we have the inverse, we can plug 6 in to get the value at f-1(6).
f-1(x) = (x - 1)/3
f-1(6) = (6 - 1)/3
f-1(6) = 5/3
The sequence
1, 3, 7, 13, 21, ...
has first-order differences
2, 4, 6, 8, ...
Let 
denote the original sequence, and 
the sequence of first-order differences. It's quite clear that
for 
. By definition of first-order differences, we have
for , or
By substitution, we have
and so on, down to
You should know that
and we're given 
, so
or
Alternatively, since we already know the sequence is supposed to be quadratic, we can look for coefficients 
such that
We have
and we can solve this system for the 3 unknowns to find 
.
