Answer:
Ok, we know that g(x) = a*f(x + b), we want to find all the transformations that we must apply to f(x) to construct g(x).
Let's assume at the beggining that T2(T1(f(x))) = g(x), and start appliying the transformations.
First, we have a horizontal shift.
If we want to move the graph A (A positive) units to the right, we should have:
g(x) = f(x - A)
in this case we have
g(x) = f(x + b) = f(x - (-b))
So we have a shift of -b units to the right, or b units to the left.
Second:
We have a vertical contraction/dilation.
if we have a function f(x), a compression/dilation of scale factor A is written as:
g(x) = A*f(x)
if A > 1, we have a dilation.
if 0 < A < 1, we have a contraction.
In this case the scale factor is a.
g(x) = a*f(x).
Now, applying both transformations we have:
> shift of b units to the left.
> contraction/dilation of scale factor a.
g(x) = a*f(x +b)
The reciprocal of 1/6 is 6/1 or 6
The product of reciprocals equals 1