Find the range for the function

In summary, the range of the original function is all the reals, but the range of the inverse function changes depending on the value of x.
  • #1
jesuslovesu
198
0
I have y = ln(2x^3 + e) / 2
and I need to find the range for the function.

So I proceed to find the inverse [ ( e^(2x) - e ) / 2 ] ^ (1/3) = y
my memory is a little sketchy but don't I need to put the domain boundary value for the original into the inverse to find the range (apparently not because my graphing calc shows otherwise). -- If not does that mean the range of the original function is all real numbers?
 
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  • #2
i think the easiest way to find the domain or range is to know them for the basic functions, then apply your function to those. ie, what you have is a logarthimic function. so, the range of a typical log function is all reals right? what about your equation would change that? (nothing..)

why did you decide to graph the inverse? its true that the range of the original function will be the domain of its inverse. for a log function the domain is only positive reals, the range, as we've found is all reals. for the exponential its the opposite, domain is all reals and range is positive.
 
  • #3
jesuslovesu said:
I have y = ln(2x^3 + e) / 2
and I need to find the range for the function.

So I proceed to find the inverse [ ( e^(2x) - e ) / 2 ] ^ (1/3) = y
my memory is a little sketchy but don't I need to put the domain boundary value for the original into the inverse to find the range (apparently not because my graphing calc shows otherwise). -- If not does that mean the range of the original function is all real numbers?
Okay, so the domain for the function ln(x) is x > 0, and the range of the function is all the reals, right?
So now, the range of (2x3 + e) is all the reals right? And ln(2x3 + e) is only defined for (2x3 + e) > 0. So what can you say about the range of ln(2x3 + e)?
Can you go from here? :)
 

1. What is the definition of range in a function?

The range of a function refers to the set of all possible output values of the function. In other words, it is the collection of all values that the function can produce.

2. How do you find the range for a given function?

To find the range of a function, you can either graph the function and determine the vertical spread of the points, or you can use algebraic methods such as substitution and solving for the output variable.

3. Can a function have an infinite range?

Yes, a function can have an infinite range if there is no limit to the possible output values. This is common with functions such as exponential or logarithmic functions.

4. Is the range of a function always the same as the domain?

No, the range and domain of a function are two different sets of values. The domain refers to the input values, while the range refers to the output values. It is possible for the range to overlap with the domain, but they are not always the same.

5. Why is it important to find the range of a function?

Knowing the range of a function can help us understand its behavior and make predictions about its output values. It can also help us determine if a function is one-to-one or onto, which can be useful in solving mathematical problems.

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