1. ## Simple Exponential Equation

f(x) = 2 + 3x

What is f(2x) - f(x)?
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2. ## Re: Simple Exponential Equation

What have you done ?
First : f(2x)= ?

3. ## Re: Simple Exponential Equation

I'm assuming that f(2x) = 2(2+3x)?

4. ## Re: Simple Exponential Equation

No. f(x) is a notation that says "the function operated on the value x". Here we are told \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?

5. ## Re: Simple Exponential Equation

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)= ?

6. ## Re: Simple Exponential Equation

Ah, thank you. Such a noob mistake.

No

8. ## Re: Simple Exponential Equation

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

9. ## Re: Simple Exponential Equation

Tie breaker: " $3^x(3^x- 1)$" 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)".

10. ## Re: Simple Exponential Equation

OK. This is what I meant.

11. ## Re: Simple Exponential Equation

Originally Posted by HallsofIvy
Tie breaker: " $3^x(3^x- 1)$" 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 " $(3^x)^2 -3^x$"

12. ## Re: Simple Exponential Equation

Originally Posted by votan
or " $(3^x)^2 -3^x$"
Use this identity to prove the 1 = 2. No kidding. It's real.