SOLUTION: Assume that f(3) = 4. Name a point that must be on the graph of y= -5f(2x - 3) + 1

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Question 1208022: Assume that f(3) = 4. Name a point that must be on the graph of y= -5f(2x - 3) + 1
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
Assume that f(3) = 4. Name a point that must be on the graph of y= -5f(2x - 3) + 1
~~~~~~~~~~~~~~~~~~~~~~~~

First, we want the argument 2x-3 be 3.


So, we write this equation

    2x - 3 = 3.


Then we solve it  and find  x =  =  = 3.



Next,  we want to calculate  y = -5f(2x-3) + 1.

We just know that 2x-3 is 3, because we found x in this way.
So, we write

    y = = -5f(3) + 1 = (at this point, we know and use that f(3)=4, so we continue) = -5*4 + 1 = -20 + 1 = -19.



Thus the point  (x,y) = (3,-19)  is on the graph  y = -5f(2x-3) + 1.


ANSWER.  If f(3) = 4,  then the point which must be on the graph  y = -5f(2x-3) + 1  is  (x,y) = (3,-19).

Solved.


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It is a real      for you to solve many other similar problems.


        To start,  you should say to yourself  "First,  we want . . . "

                These words are magic.

        As soon as you pronounce them,  all necessary words and thoughts that follow,  will flow by themselves.


////////////////////


To see other similar solved problems, look into the lesson
    - Given a point on a plot of a function, find the corresponding point on the plot of transformed function
in this site.

It is to make your horizon wider.



Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

I'll go over a similar example.

Problem
Given f(4) = 5
Find a point on g(x) = 2*f(3x+1) + 7
Solution

Compare f(4) with f(3x+1)
Equate the inputs and solve for x.
4 = 3x+1
3x = 4-1
3x = 3
x = 3/3
x = 1
Therefore x = 1 leads to 3x+1 = 4.
If x = 1 then f(3x+1) = f(4) = 5.

Then,
g(x) = 2*f(3x+1) + 7
g(1) = 2*f(3*1+1) + 7
g(1) = 2*f(4) + 7
g(1) = 2*5 + 7
g(1) = 10 + 7
g(1) = 17
We have shown that (1,17) is on g(x).
Keep in mind this is likely not the final answer to your particular question, but you can use it as a template to solve.

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