# Simple Exponential Equation

• Sep 15th 2013, 09:56 PM
Fratricide
Simple Exponential Equation
f(x) = 2 + 3x

What is f(2x) - f(x)?
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• Sep 15th 2013, 10:02 PM
JJacquelin
Re: Simple Exponential Equation
What have you done ?
First : f(2x)= ?
• Sep 15th 2013, 10:12 PM
Fratricide
Re: Simple Exponential Equation
I'm assuming that f(2x) = 2(2+3x)?
• Sep 15th 2013, 11:13 PM
Prove It
Re: Simple Exponential Equation
No. f(x) is a notation that says "the function operated on the value x". Here we are told \displaystyle \displaystyle \begin{align*} f(x) = 2 + 3^x \end{align*}, which says that whatever value you put in, is what you will raise 3 to the power of, and then add 2 to. So if instead we put in 2x we get f(2x). If the same function operates on 2x (so this is what we raise 3 to the power of and then add 2 to), what will we get?
• Sep 15th 2013, 11:34 PM
JJacquelin
Re: Simple Exponential Equation
Quote:

Originally Posted by Fratricide
I'm assuming that f(2x) = 2(2+3x)?

No, you are confusing 2f(x) with f(2x).
f(x) = 2+3x
It is true for any symbol, for example :
f(v) = 2+3v
or, for example :
f(t) = 2+3t
Your difficulty is to understand that t=2x in the case of f(2x)
Then, f(2x)= ?
• Sep 16th 2013, 03:42 AM
Fratricide
Re: Simple Exponential Equation
Ah, thank you. Such a noob mistake.

• Sep 16th 2013, 05:02 AM
Prove It
Re: Simple Exponential Equation
No
• Sep 16th 2013, 09:46 AM
JJacquelin
Re: Simple Exponential Equation
Quote:

Originally Posted by Fratricide
Ah, thank you. Such a noob mistake.

Yes
• Sep 16th 2013, 11:36 AM
HallsofIvy
Re: Simple Exponential Equation
Tie breaker: "$\displaystyle 3^x(3^x- 1)$" is the correct answer to the original question "what is f(2x)- f(x)". It is NOT the correct answer to the last question "what is f(2x)".
• Sep 16th 2013, 12:40 PM
JJacquelin
Re: Simple Exponential Equation
OK. This is what I meant.
• Sep 17th 2013, 06:41 PM
votan
Re: Simple Exponential Equation
Quote:

Originally Posted by HallsofIvy
Tie breaker: "$\displaystyle 3^x(3^x- 1)$" is the correct answer to the original question "what is f(2x)- f(x)". It is NOT the correct answer to the last question "what is f(2x)".

or "$\displaystyle (3^x)^2 -3^x$"
• Sep 20th 2013, 05:20 PM
votan
Re: Simple Exponential Equation
Quote:

Originally Posted by votan
or "$\displaystyle (3^x)^2 -3^x$"

Use this identity to prove the 1 = 2. No kidding. It's real.