What are the values of x for f(x) = g(x)?

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Discussion Overview

The discussion revolves around finding the values of x for which the functions f(x) and g(x) are equal, specifically f(x) = x² and g(x) = 10 - 3x. The scope includes mathematical reasoning and problem-solving strategies related to quadratic equations.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in starting the problem and seeks guidance on how to approach it.
  • Another participant suggests setting the equations equal to each other, leading to the equation x² + 3x - 10 = 0.
  • There is a discussion about whether to substitute f(x) into g(x) or vice versa, with some uncertainty about the correctness of this approach.
  • Participants mention the possibility of solving the resulting quadratic equation using the quadratic formula or by inspection.

Areas of Agreement / Disagreement

Participants generally agree on the method of setting the functions equal to each other, but there is some uncertainty regarding the substitution process and the best approach to solving the equation.

Contextual Notes

There are missing assumptions regarding the methods of solving the quadratic equation and the participants' familiarity with the quadratic formula. The discussion does not resolve the best approach to finding the values of x.

Iwanttolearn1
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Hello, mathhelpboards. I'm having trouble solving this problem on my review but can't figure out how to start it.

Find the values of x for which f(x) = g(x).

f(x) = x^2 , g(x) = 10 - 3x.

It seems like its easy but I can't really pick out what to put what where.
 
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Iwanttolearn said:
Hello, mathhelpboards. I'm having trouble solving this problem on my review but can't figure out how to start it.

Find the values of x for which f(x) = g(x).

f(x) = x^2 , g(x) = 10 - 3x.

It seems like its easy but I can't really pick out what to put what where.

Hey Iwanttolearn! Welcome to MHB! ;)

Let's see...
\[
f(x)=g(x) \Rightarrow x^2=10-3x \Rightarrow x^2+3x-10=0
\]
For which $x$ would that be the case? (Wondering)
 
I like Serena said:
Hey Iwanttolearn! Welcome to MHB! ;)

Let's see...
\[
f(x)=g(x) \Rightarrow x^2=10-3x \Rightarrow x^2+3x-10=0
\]
For which $x$ would that be the case? (Wondering)

So you would put the f(x) value into the g(x)? I think that looks right or either I'm completely wrong.
 
Iwanttolearn said:
So you would put the f(x) value into the g(x)? I think that looks right or either I'm completely wrong.

We're replacing the occurences of $f(x)$ and $g(x)$ by their respective definitions.
That gives us an equation we can solve with the quadratic formula, or just with inspection...
 
I like Serena said:
We're replacing the occurences of $f(x)$ and $g(x)$ by their respective definitions.
That gives us an equation we can solve with the quadratic formula, or just with inspection...

Oh wow! I get it now. Many thanks your way!(Handshake)(Happy)
 

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