Question 1208030
<pre>
Manipulations are hard to understand without visual interpretations.
Here is a visual illustration of this problem with the
case {{{y}}}{{{""=""}}}{{{sqrt(x)}}}

We begin with 
{{{y}}}{{{""=""}}}{{{sqrt(x)}}}

{{{drawing(400,4800/17,-2,15,-2,10, 
graph(400,4800/17,-2,15,-2,10, 17,18,sqrt(x)) )}}}

Then we stretched it horizontally by a factor of 2,
giving us the graph of

{{{y}}}{{{""=""}}}{{{sqrt(expr(1/2)x)}}} 

{{{drawing(400,4800/17,-2,15,-2,10, 
graph(400,4800/17,-2,15,-2,10,18,17,sqrt(x/2)) )}}}

Then we shifted it right 1 unit, giving us the graph of

{{{y}}}{{{""=""}}}{{{sqrt(expr(1/2)(x-1))}}} 

{{{drawing(400,4800/17,-2,15,-2,10, 
graph(400,4800/17,-2,15,-2,10,18,17,sqrt((1/2)(x-1))) )}}}

Then finally we stretched the graph vertically by a factor
of 3, giving us the final graph of {{{y}}}{{{""=""}}}{{{3*sqrt(expr(1/2)(x-1)))}}}

{{{drawing(400,4800/17,-2,15,-2,10, 
graph(400,4800/17,-2,15,-2,10,18,17,3sqrt((1/2)(x-1))) )}}}

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

Here are the graphs of f(x) and g(x), the red one is f(x),
and the blue graph is g(x).

{{{drawing(400,4800/17,-2,15,-2,10, 
circle(4,2,.1), circle(9,6,.1),
locate(4,2,"(4,2)"), locate(9,6,"(9,6)"),
graph(400,4800/17,-2,15,-2,10, sqrt(x)),
graph(400,4800/17,-2,15,-2,10,17,18,3sqrt((1/2)(x-1))) ))}}}

The point (4,2) lies on the graph of y = f(x), so the point (2•4+1, 3•2),
or (9,6) lies on the graph of y = g(x)

Edwin</pre>