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

 Jun 4, 2024
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why does this look like a problem from AoPS

i hope you aren't trying to cheat on your homework

if you are i'll still give it but at least read the solution and understand it

kay

so

 

We don't know any other possible outputs from any possible inputs from f(x), so we can only assume that in order to simplify f(x), we have to make the input equal to 3. This gives 5x + 5 = 3, which simplifies to x = -0.4. Then, since f(3) = 4, we have 1/5 * 4 - 5 = 0.8 - 5 = -4.2.

 

Since the input is -0.4 and the output is -4.2, a point that must be on the graph of f(x) is (-2/5, -21/5).

 Jun 4, 2024

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