Algebra Inverse Function Problem

In summary, the conversation discusses the concept of finding the inverse form of the function f(x)=(x-3)^2 -1 when the condition x≥3 is present. The speaker is seeking clarification on how this condition affects the inverse form and suggests that it sets a domain limit. The summary also mentions that the conversation touched on the steps needed to solve the equation y=(x-3)^2 -1 for x.
  • #1
nordqvist11
15
0

Homework Statement


f(x)=(x-3)^2 -1 for x ≥3


Homework Equations





The Attempt at a Solution


I am having difficulty grasping the concept of changing the greater than or equal to part of the equation above to it's inverse form. If for x it says x≥3 then how would that statement be relevant to finding the inverse of the function. In other words, I need clarification as to how that specific aspect of the equation changes in inverse form.
 
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  • #2
Well, what does the condition x≥3 mean for the equation f(x)=(x-3)^2 -1 ?
 
  • #3
That the domain is limited and does not include all real numbers for the function. I guess it sets a domain limit?
 
  • #4
Show what steps are needed to solve y=(x-3)2 -1 for x.
 

FAQ: Algebra Inverse Function Problem

What is an inverse function?

An inverse function is a function that reverses the effect of another function. In other words, if a function f(a) produces a certain output b, the inverse function f^-1(b) will produce the original input a.

How do you find the inverse of a function?

To find the inverse of a function, switch the x and y variables and solve for y. This will give you the inverse function in terms of x. It is important to check if the inverse function is still a valid function by making sure it passes the vertical line test.

Why is finding the inverse of a function important?

Finding the inverse of a function is important because it allows us to solve for the original input when given the output. This is useful in various real-world applications, such as in finance, physics, and engineering. It also helps in simplifying complex equations and solving for unknown variables.

What are the properties of inverse functions?

The main properties of inverse functions are that they are symmetric, meaning that the inverse of the inverse function is the original function, and that they have the same domain and range as the original function. Additionally, the composition of a function and its inverse will result in the identity function.

What are some common mistakes when solving algebra inverse function problems?

Some common mistakes when solving algebra inverse function problems include forgetting to switch the x and y variables, not checking if the inverse function is still a valid function, and incorrectly simplifying the equation. It is important to carefully follow the steps and double-check your work to avoid these mistakes.

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