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

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  • Thread starter Iwanttolearn1
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In summary, the conversation discusses finding the values of x for which f(x) = g(x), with f(x) = x^2 and g(x) = 10 - 3x. The problem is solved by replacing f(x) and g(x) with their definitions and solving the resulting equation using the quadratic formula or inspection.
  • #1
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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  • #2
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)
 
  • #3
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.
 
  • #4
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...
 
  • #5
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)
 

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

How do I find the value of x in an equation?

To find the value of x in an equation, you need to isolate the variable x on one side of the equation by performing the same operations on both sides. This means using inverse operations such as addition, subtraction, multiplication, or division to get rid of any constants or other variables present.

What is the order of operations when finding the value of x?

The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction), should be followed when solving for x. This ensures that the correct operations are performed in the correct order to get the accurate value of x.

Can I use a calculator to find the value of x?

Yes, a calculator can be a useful tool when solving for x. However, it is important to check your work and understand the steps taken to find the value of x, rather than relying solely on the calculator.

Are there any special cases when finding the value of x?

Yes, some equations may have multiple solutions for x or may have no solutions at all. It is important to carefully analyze the equation and follow the appropriate steps to find the correct value of x, if it exists.

How do I know if I have found the correct value of x?

You can check your answer by plugging it back into the original equation and seeing if it satisfies the equation. If it does, then you have found the correct value of x. If not, you may need to go back and check your work or try a different approach.

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