Finding function given new input

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Discussion Overview

The discussion revolves around finding the value of the function f given a new input, specifically f(3z), based on the defined function f(x) = x^2 + 5. The scope includes mathematical reasoning and function evaluation.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant asks how to find f(3z) based on the function definition.
  • Another participant suggests replacing x with 3z in the function definition and simplifying.
  • A participant incorrectly states that f(3z) equals 5, expressing uncertainty about their understanding.
  • A later reply clarifies the function definition and provides an example with a different input, 4u, to illustrate the process of squaring the input and adding 5.
  • One participant proposes that f(3z) equals 3x^2 + 5 = 9z^2 + 5, questioning if this is correct.
  • Another participant confirms the end result but corrects the notation, emphasizing that f(3z) should be expressed as (3z)^2 + 5 = 9z^2 + 5.
  • A participant expresses gratitude for the clarification.
  • A moderator reminds participants to avoid tagging new questions onto existing threads to maintain clarity.

Areas of Agreement / Disagreement

Participants generally agree on the method of evaluating the function but there is some confusion regarding the notation and initial claims about the value of f(3z.

Contextual Notes

Some participants express uncertainty about their understanding of the function evaluation process, and there are unresolved issues regarding the correct notation and simplification steps.

zolton5971
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The function f is defined by f(x)=x^2+5

Find f(3z)

How do I find f(3z)
 
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Everywhere in the definition of $f(x)$, where you see an $x$, replace it with a $3z$, and then simplify as needed. What do you find?
 
f(3z)=5

I'm not sure I not very good at this.
 
We are given the definition:

$$f(x)=x^2+5$$

Notice that in the definition, we are told to take the input, square it, and then add 5. So, say the input is $4u$, then we need to square that, which is $(4u)^2$, and then add 5, so that we have $(4u)^2+5$. Hence:

$$f(4u)=(4u)^2+5=4^2u^2+5=16u^2+5$$

Can you now find $f(3z)$?
 
f(3z)=3x^2+5= 9z^2+5 is that close?
 
zolton5971 said:
f(3z)=3x^2+5= 9z^2+5 is that close?

You have the right end result, but what you want to write is:

$$f(3z)=(3z)^2+5=9z^2+5$$
 
Ok thanks!
 
I have again moved a new question of yours into a new thread. Please don't tag a new question onto an existing thread, as this can cause threads to become convoluted and hard to follow. Also, your new question will be seen by more people if you begin a new thread for it. :D
 

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