Question 1208030
<pre>

This type of problem requires knowing how to shift graphs right and 
left, stretching and shrinking, both horizontally and vertically.
It is also necessary that the transformations are done in the right
order, multiplications first then additions and subtractions.

Vertical transformations are done to the function itself, the whole
"right side".

Vertical transformations are as they seem, adding and subtracting
to shift up and down, multiplying by factors > 1 to stretch, 
multiplying by factors < 1 to shrink.
  
Horizontal transformation are done to x.

Horizontal transformation are "backward" from what they seem, adding
to x to shift left, subtracting from x to shift right, multiplying
by the reciprocal of factors > 1 to stretch, and multiplying by 
factors > 1 to shrink.

Since the x-value of f(x) is 'a' and the x-value on g(x) is '2a+1',
the factor of 2 in '2a+1' means that the graph of f(x) is stretched 
horizontally by a factor of 2, which means we multiply x by the
reciprocal of 2, which is 1/2. 

So doing only that horizontal stretch would give us {{{f(expr(1/2)x)}}}

Then the term +1 in '2a+1' means that we shift the graph right by 1 unit,
which means we subtract 1 from x or, add -1 to x

so doing that would give us {{{f(expr(1/2)(x-1))}}}

That finishes doing everything required to do to the x-coordinate.

Now the 3 factor in "3b" means that the graph is stretched vertically by
a factor of 3, so we multiply the entire function by 3.

That gives us {{{3*f(expr(1/2)(x-1))}}}

So the answer is

{{{g(x)}}}{{{""=""}}}{{{3*f(expr(1/2)(x-1))}}}

Edwin</pre>