Find g(4) When f(4)-5 and lim[5f(x)-g(x)]=5

In summary, the conversation discusses finding the value of g(4) given that f and g are continuous functions with f(4)-5 and the limit of [5f(x)-g(x)] as x approaches 4 is 5. The conversation also highlights the importance of clearly presenting the problem with accurate use of symbols.
  • #1
step1536
19
0

If f and g are continuous functions with f(4)-5 and lim [5f(x) -g(x) ]=5 find g(4)
x-->4
 
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  • #2


It's a bit tough to read what's going on here

Is this supposed to be f(4)=5? the limit as x goes to 4 of [5f(x)-g(x)]=5? And you want to find g(4)?

If so, you should be able to manipulate your limit equation using algebra of limit rules (for example, lim(a+b) = lim(a) + lim(b)). Then you need to know what happens to a continuous function when you have it inside of a limit. What do you think happens?
 
  • #3


step1536 said:
If f and g are continuous functions with f(4)-5 and lim [5f(x) -g(x) ]=5 find g(4)
x-->4

Aside from the confusion over whether you're saying that f(4) = -5 or f(4) = 5, do you want g(4) or [itex]\lim_{x \rightarrow 4} g(x)[/itex]?

If you want to get help, you really need to concentrate on presenting your problem so that people can understand what you're asking. That would include spending some time on learning what the relevant symbols mean.
 

What is g(4)?

g(4) is the value of the function g at x=4.

How is g(4) related to f(4)?

In this case, since f(4)-5, we can say that g(4)=f(4)-5.

What is the limit of [5f(x)-g(x)] as x approaches 4?

The limit of [5f(x)-g(x)] as x approaches 4 is equal to 5.

Can we find the exact value of g(4) using the given information?

No, we cannot find the exact value of g(4) with just this information. We need to know either the value of f(4) or the function g(x) in order to determine the exact value of g(4).

What does this information tell us about the behavior of g(x) near x=4?

This information tells us that as x approaches 4, the value of g(x) approaches 5. It also tells us that g(x) is related to f(x) in a specific way, where g(x) is always 5 less than f(x).

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