Question 1167049
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The function f(x) is transformed to produce a function g(x) where g(x) = −2f(5x)−5. 
If (−9,4) is a point on the graph of f(x), give the coordinates of the transformed point on the graph if g(x).
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<pre>
The fact that (-9,4) is a point on the graph of f(x) means that

    4 = f(-9).


Now, you need to have -9 = 5x,  so for it you take x = {{{-9/5}}}.


It provides you f(5x) = {{{f(5*(-9/5))}}} = f(-9) = 4.    (1)


Next, according to the definition  g(x) = -2f(5x) - 4,

you should multiply the '4'  in  (1)  by (-2) and subtract 5 from the product.


It gives you the ordinate y = (-2)*4 - 5 = -8 - 5 = -13.


Thus the required point  (x,y)  is  ({{{-9/5}}},{{{-13}}}).


This point is the transformed point on the graph of g(x).
</pre>

At this point, the problem is solved completely.


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This problem is a standard/typical problem on analyzing points on transformed graphs,
and my solution is a standard reasoning to solve such problems.