Find The Range And Inverse (please Help I Have Test Monday)

In summary, to find the range and inverse of the function f(x) = square root of [(8x^2 +1)/ (9-5x^2)], first understand that the range is all the values f(x) can take and the inverse of a function is the function that cancels it out. To find the inverse function, swap the y's and x's and solve for x in terms of y. The range can easily be solved by taking the square root of the function and ensuring the radicand is not negative.
  • #1
STAR3URY
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I don't understand this at all...

Find the Range and Inverse of f(x) = square root of [(8x^2 +1)/ (9-5x^2)]


I am so confused please help!
 
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  • #2
The range of a function is all the values f(x) can take. The inverse of a function is basically the function that cancels it out. The inverse of division by 3 is multiplication by 3. The inverse of square rooting a positive number is squaring that number. To find the inverse function when you have a general [tex]y=f(x)[/tex] is to swap the y's and x's, ie [tex]x=f(y)[/tex], and it is not necessarily required to solve again for y, and in general it is not even possible in terms of elementary functions, but sometimes you lose marks when you can but you don't.
 
  • #3
The range is easily solvable because only x^2 terms exist. Solving for x in terms of y can thus be done by a simple square root. Just make sure the radicand is not negative and that will give you the restrictions for the range y.
 

1. What is the range of a function?

The range of a function is the set of all possible output values that the function can produce. It is also referred to as the "y-values" of the function.

2. How do you find the range of a function?

To find the range of a function, you can graph the function and look at the values on the y-axis. Alternatively, you can also plug in different values for the input and observe the corresponding output values. The set of all the output values will be the range of the function.

3. What is an inverse function?

An inverse function is a function that "undoes" the original function. In other words, if you input the output of a function into its inverse, you will get back the original input. The inverse function is denoted by f-1.

4. How do you find the inverse of a function?

To find the inverse of a function, you can follow these steps:1. Solve the function for y.2. Swap the x and y variables.3. Replace y with f-1(x) to get the inverse function.

5. Can every function have an inverse?

No, not every function has an inverse. For a function to have an inverse, it must be a one-to-one function, meaning that each input has a unique output. If a function has multiple outputs for the same input, it does not have an inverse.

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