1. The function f(x) is not defined for x = 0. It has the property

In summary, the conversation discusses two functions, f(x) and f, and their properties. The first function, f(x), is not defined for x = 0 and has the property that for all nonzero real numbers x, f(x) + 2f(1/x) = 3x. The second function, f, is defined by f(x) = (ax+b)/(cx+d) and has the properties f(19) = 19, f(97) = 97, and f(f(x)) = x for all values of x except -d/c. The conversation prompts the listener to find all values of a such that f(a) = f(-a) and to find the unique number that is not
  • #1
awkwardnerd
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1. The function f(x) is not defined for x = 0. It has the property that for all nonzero real numbers x, f(x) + 2f(1/x) = 3x. Find all values of a such that f(a) = f(-a)

2. The function f is defined by f(x) = (ax+b)/(cx+d), where a, b, c, and d are nonzero real numbers, and has the properties: f(19) = 19, f(97) = 97, and f(f(x) = x for all values of x except -d/c. Find the unique number that is not in the range of f.

First time seeing this. Somehow tell me how to approach it, I don't need the answer.
 
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  • #2


1. Try to isolate f(x) by using the equation you have by setting ing y = 1/x.

2. Obviously, since f(f(x)) = x for all x /= -d/c, the number have to be -d/c. How can you find this value?
 

1. What does it mean when the function f(x) is not defined for x = 0?

When a function is not defined for a certain value of x, it means that the function does not have a corresponding output for that particular input. In other words, the function does not have a defined value at x = 0.

2. Why is the function f(x) not defined for x = 0?

The function may not be defined for x = 0 due to various reasons such as division by zero, logarithms of non-positive numbers, or square roots of negative numbers. These values would result in an undefined output, hence the function is not defined for x = 0.

3. Can the function f(x) be defined for x = 0?

It depends on the specific function and its properties. Some functions can be modified or extended to include x = 0 in their domain, while others cannot. It is important to consider the properties of the function before determining if it can be defined for x = 0.

4. How do I know if a function is not defined for x = 0?

You can determine if a function is not defined for x = 0 by looking at its domain. If x = 0 is not included in the domain, then the function is not defined for that value. You can also plug in x = 0 into the function and see if it results in an undefined output.

5. What is the significance of a function not being defined for x = 0?

The significance of a function not being defined for x = 0 is that it limits the range of inputs for which the function can be evaluated. It also means that the function may have certain restrictions or limitations in its behavior, and it is important to understand and consider these when working with the function.

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