Image of Function h: (0,1)→ ℝ - 65 characters

So in this problem, you are looking for values of x such that h(x)=0. The only value of x that makes this work is x=-4, so the image of the function is just {-4}.In summary, the image of the function h(x) = 1/(x2+8x) for 0<x<1 is {-4}.
  • #1
mrchris
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Homework Statement


find the image of the function
h: (0,1)→ ℝ defined by h(x) = 1/(x2+8x) for 0<x<1

Homework Equations


The Attempt at a Solution


I have tried a number of things, I can see the answer intuitively but I am having trouble with the proof. I set the function up as 1/(x2+8x)=b, and I have been trying to manipulate this in order to get what I need. the first thing i did was calculate b at x=0 (undefined) and x=1 (1/9) and from there I got 3 different intervals for b, the last one (1/9, ∞) i know is correct. I just am not sure how to show this is correct.

Homework Statement


Homework Equations


The Attempt at a Solution

 
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  • #2
Here is one basic fact you need here- the fraction f(x)/g(x) is equal to 0 if and only if the numerator, f(x), is 0.
 

FAQ: Image of Function h: (0,1)→ ℝ - 65 characters

1. What does the notation (0,1)→ ℝ mean?

The notation (0,1)→ ℝ represents a function with a domain of all real numbers between 0 and 1, and a range of all real numbers.

2. What does the "h" in the function represent?

The "h" in the function represents the name given to the function. It is used to identify the specific function being discussed.

3. What is the purpose of the image of function h?

The image of function h is the set of all output values that can be produced by function h. It represents all possible values that can be obtained by plugging in values from the domain of function h.

4. Can the image of function h be a subset of the real numbers?

Yes, the image of function h can be a subset of the real numbers. This means that not all real numbers between 0 and 1 may be output values of function h.

5. How is the image of function h different from the domain and range?

The domain of function h represents all possible input values, while the range represents all possible output values. The image of function h is a subset of the range, and represents only the actual output values that are produced by function h.

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