Piecewise Function

[Jacob]

f(x) = 2x + 1 / 3x - 6 is continuous at x = 2


How do I change this fraction function into a piecewise function to define the existence?

 

[topsquark]

First, I suspect your function should be written as f(x) = (2x + 1)/(3x - 6).

Second, we know that the function does not exist at x = 2 so your domains would have to be \(\displaystyle ( - \infty, ~2)\) and \(\displaystyle (2, ~ \infty )\).

That's most of it. Can you finish?

-Dan

 

[Dr.Peterson]

f(x) = 2x + 1 / 3x - 6 is continuous at x = 2

How do I change this fraction function into a piecewise function to define the existence?

If the added parentheses are correct, the problem makes no sense as stated. The functon is not continuous, and nothing can make it so.

Please coy the problem word for word as given to you.

 

[Jacob]

If the added parentheses are correct, the problem makes no sense as stated. The function is not continuous, and nothing can make it so.

Please coy the problem word for word as given to you.

Decide whether f(x) = 2x + 1 / 3x - 6 is continuous at x = 2. There is no parentheses in this question.
If the question were asked in Piecewise function then I know how to solve since it is given in fraction I have no idea how I can solve this.

 

[Dr.Peterson]

So you did copy the question wrong; it didn't state that f is continuous, but asked whether it is! There is no piecewise function in this problem; the answer is simply that it is not continuous, because it is not even defined at x=2.

Parentheses are needed when you rewrite a fraction horizontally.

 

[ksdhart2]

the answer is simply that it is not continuous, because it is not even defined at x=2.

This is most likely the intended answer... However, if we interpret the function exactly as written:

\(\displaystyle 2x + 1 / 3x - 6 = 2x + \frac{1}{3}x - 6 = \frac{7x - 18}{3}\)

Then the function is continuous everywhere.

 

[Jacob]

So you did copy the question wrong; it didn't state that f is continuous, but asked whether it is! There is no piecewise function in this problem; the answer is simply that it is not continuous, because it is not even defined at x=2.

Parentheses are needed when you rewrite a fraction horizontally.

Thank you. Sorry, I have confused myself. Thanks for clarify