Value of x for which f(x) is undefined

[Richie Smash]

Homework Statement

Given $$f(x)=\frac{3x-2}{x+1}$$
Calculate the value of x, for which f(x) is undefined.

Homework Equations

The Attempt at a Solution

Hi, I've never come across this before and I'm not finding anything on the internet, I would post my attempt but the problem is I don't know where to start.

What does it mean by undefined, my best guess is that it isn't equal to anything?

 

[berkeman]

Homework Statement

Given $$f(x)=\frac{3x-2}{x+1}$$
Calculate the value of x, for which f(x) is undefined.

Homework Equations

The Attempt at a Solution

Hi, I've never come across this before and I'm not finding anything on the internet, I would post my attempt but the problem is I don't know where to start.

What does it mean by undefined, my best guess is that it isn't equal to anything?

One definition of undefined would be f(x) = ∞

What value of x would satisfy that?

 

[Richie Smash]

Well, if y=∞, then it would the be everything above 0 and also including 0?

 

[berkeman]

One definition of undefined

I just realized the irony in my reply...

 

[berkeman]

Well, if y=∞

y? Why y?

 

[Richie Smash]

Because f(x) can be represented as y as far as I know.

 

[berkeman]

Because f(x) can be represented as y as far as I know.

y didn't you show that in your post? y, oh y?!

Anyway, only where the function goes to infinity would it be considered "undefined". And that would be where?

 

[Richie Smash]

y didn't you show that in your post? y, oh y?!

Anyway, only where the function goes to infinity would it be considered "undefined". And that would be where?

Hmm well it has to be from.. 0 to infinity.

 

[berkeman]

Hmm well it has to be from.. 0 to infinity.

$$f(x)=\frac{3x-2}{x+1}$$

So x=-1 gives f(x) = infinity, why is that?

 

[Richie Smash]

Because you'd end up dividing by 0

 

[PeterDonis]

What does it mean by undefined

It means that in order to calculate the value of $f(x)$, you would have to perform a mathematical operation that is not allowed. A value of $x$ has already been mentioned that would require you to do that. (Hint: the expression $f(x) = \infty$ is really a sloppy way of saying "you would have to perform a mathematical operation that is not allowed". And you've already mentioned the operation as well.)

Because f(x) can be represented as y

This is just playing with symbols; it has no mathematical meaning. You already have an expression for $f(x)$; you don't need any other symbols.

 

[Mark44]

So x=-1 gives f(x) = infinity, why is that?

No, not true.
If x = -1, there is division by zero, making the fraction undefined. f(-1) is not $\infty$.
Looking a bit ahead from the scope of the OP's problem, as x approaches -1 from the left, you get completely different values from when x approaches -1 from the right. On one side of -1, the graph of this function goes off to $-\infty$ while on the other side of -1, the graph goes off to $+\infty$.

 

[Richie Smash]

OK I see that -1 is the answer, as it will indeed make the function undefined, but my problem is I'm just guessing a number and putting it in the function, how do I actually calculate it?

 

[Mark44]

Given $f(x)=\frac{3x-2}{x+1}$
Calculate the value of x, for which f(x) is undefined.

OK I see that -1 is the answer, as it will indeed make the function undefined, but my problem is I'm just guessing a number and putting it in the function, how do I actually calculate it?

What's to guess? Division by zero is undefined, so what value of x causes the fraction to be undefined? In your problem, the denominator is zero when x + 1 = 0, or equivalently, when x = -1.

For many problems like this, a rational function will be undefined for any input value that makes the denominator zero. Other things to look out for are square root and even-root functions for which the argument is negative, or log functions for which the argument is nonpositive.