Help writing an equation that satisfies some statements

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In summary, the conversation discusses how to approach writing an equation that satisfies multiple conditions simultaneously. The conditions include a specific domain, continuity on the domain, and specific limits at x = 1. The attempt at a solution involves using a fraction, but the question itself is inconsistent as the given conditions would make the function discontinuous at x = 1.
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ammsa
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Homework Statement


how do u approach a question like that?

write an equation that satisfy the following simultaneously

a) the domain of f is (-Infinity, 0) U (0,infinity)
b) f is continuous on its domain (that is everywhere except at x = 0)
c) lim f(x) as x--> 1- (from the left) = - infinti
d) lim f(x) as x --> 1+ (from the right) = 0
e) f(1) = 2.



The Attempt at a Solution



i know from the domain that x can't be zero
so the equation is probably going to a fraction, let say (x+1)/x.
(x+1)/x domain is (-Infinity, 0) U (0,infinity) and its continuous on its domain.
f(1) = (1+1)/1 = 2/1 = 2.
so a, b, and e are correct
but c and d, i don't know how to do them.
any help?
 
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  • #2
welcome to pf!

hi ammsa! welcome to pf! :smile:

(have an infinity: ∞ :wink:)
ammsa said:
a) the domain of f is (-Infinity, 0) U (0,infinity)
b) f is continuous on its domain (that is everywhere except at x = 0)
c) lim f(x) as x--> 1- (from the left) = - infinti
d) lim f(x) as x --> 1+ (from the right) = 0
e) f(1) = 2.

no, the question must be wrong :redface:

"b) f is continuous on its domain (that is everywhere except at x = 0)" is inconsistent with c) d) and e) …

those three conditions clearly make the function discontinuous at x = 1 :frown:
 

1. How do I write an equation that satisfies a given statement?

To write an equation that satisfies a given statement, you first need to understand the statement and the variables involved. Then, you can use algebraic operations such as addition, subtraction, multiplication, division, and exponentiation to manipulate the variables and write an equation that satisfies the given statement.

2. What is the process for writing an equation to satisfy multiple statements?

The process for writing an equation to satisfy multiple statements is to first identify all the statements and their corresponding variables. Then, you can use algebraic operations to manipulate these variables and write an equation that satisfies all the statements simultaneously.

3. Is there a specific format or structure for writing an equation that satisfies a statement?

No, there is no specific format or structure for writing an equation that satisfies a statement. As long as the equation accurately represents the given statement and satisfies all the conditions, it can be written in any form or structure.

4. Can an equation satisfy a statement if it contains variables that are not explicitly stated in the statement?

Yes, an equation can satisfy a statement even if it contains variables that are not explicitly stated in the statement. This is because these variables may be implied or can be solved for using other relationships within the equation.

5. Are there any tips or strategies for writing an equation that satisfies a statement?

One helpful strategy for writing an equation that satisfies a statement is to start by writing down all the given information and identifying the variables involved. Then, use algebraic operations to manipulate these variables and check that the resulting equation satisfies all the conditions of the given statement. It can also be useful to double-check your work and make sure the equation makes logical sense.

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