True or False. If f is continuous at 5 and f(5)=2 and f(4)=3,

the the lim x-> 2 f(4x^2-11) = 2

the answer is true, but i do not understand why..because when i plug the numbers in im not getting what it has stated. Please explain thanks:)

When x = 2, 4x^2-11 = 5

You have been told that f(x) is continuous at x = 5, and that the value of f(5) = 2.

Therefore the answer is true.

The question is a bit confusing because you have to think of 4x^2-11 as the argument of the f(x) function.

Thanks that makes much more sense:)

Well, let's try to unravel this mathematical mystery with a touch of humor, shall we?

First, we need to understand what it means for a function to be continuous. A function is continuous at a point if the function value at that point is equal to the limit of the function as it approaches that point.

In this case, we have f(5) = 2, which tells us that the function is continuous at x = 5. But what does that have to do with lim x->2 f(4x^2-11) = 2? It seems like a mystical connection, doesn't it?

Let's break it down step by step. We want to find the limit of the function as x approaches 2, but the expression inside the function is 4x^2 - 11. So, let's substitute x = 2 into that expression.

4(2)^2 - 11 = 16 - 11 = 5

Ah, so we're not looking at x = 2 after all! We're actually looking at x = 5. This is where the magic of continuity comes into play, my friend.

Since we know that f(5) = 2, and the function is continuous at x = 5, we can conclude that the limit as x approaches 2 of f(4x^2-11) is indeed equal to 2.

So, even though we may have been fooled by the x = 2 in the expression, it actually evaluates to x = 5, and our answer is true!

Mathematics can be quite the trickster, but with a little bit of careful analysis (and perhaps a touch of humor), we can uncover its secrets. Keep up the great work, and happy math-ing!

To determine the validity of the statement, we need to understand the conditions for the given limit and how to evaluate it.

First, let's consider the function f(x). From the given information, we know that f is continuous at x = 5, f(5) = 2, and f(4) = 3. However, there is no information about the function's behavior between these values.

Now let's focus on the limit expression: lim x->2 f(4x^2 - 11).

To evaluate this limit, we need to substitute x = 2 into the expression 4x^2 - 11. This will give us a new expression, f(4(2^2) - 11) = f(16 - 11) = f(5).

Since we are given that f is continuous at x = 5 and f(5) = 2, we can conclude that the limit expression equals 2. So, the statement "lim x->2 f(4x^2-11) = 2" is indeed true.

If you are getting a different result when plugging in the numbers, it might be because you made an error in calculations or have missed some information about the function f(x) between 4 and 5.