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avatar+1406 

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

 Dec 6, 2023
 #1
avatar+259 
-1

 

Since we are given that f(3)=4 and we know that f is a function (i.e. each input x corresponds to a unique output y), we can plug in x=3 into the definition of y=1/5∗f(5x+5)−5 to get 1/5∗f(5(3)+5)−5.

 

Evaluating this expression inside out, we get 1/5∗f(20)−5. Since f(3)=4, we know that f(20)=5f(4), so we can substitute to get 1/5∗f(20)−5=1/5∗(5f(4))−5=f(4)−5=4−5=(−1,−6)​.

 Dec 6, 2023
 #2
avatar+33600 
+1

For f(5x+5) to equal 4 we must have 5x+5 = 3,  so x = -2/5.

 

At x = -2/5 we have y = 1/5 * 4 - 5  or y = -21/5 

 

So the point (-2/5, -21/5) is on the graph.   (The point can also be expressed as (-0.4, -4.2) )

 Dec 6, 2023

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