Need clarification with Inverse functions (1 Viewer)

[coyazayo]

Hey guys I have year 10 yearlies soon and one of the topic is inverse function. However I am confused in regards to restricting a domain such that inverse f(x) exists. For example when y=x^3-3x is restricted and must include zero, the answer states the domain as -1<x<1 (which excludes the stationary points). However, an inverse sine function has a domain of -1≤x≤1, where the stationary point IS included. So how do I determine the domain?? Do I include or exclude the stationary points?

 

[He-Mann]

Don't include local maxima and minima because those make a function not one-to-one (therefore cannot have an inverse), or intuitively, does not satisfy the horizontal line test (draw horizontal line and at most one point is intercepted).

Inverse sine does have a stationary point but it's a horizontal point of inflection (I think) therefore passes the horizontal line test.

 

[braintic]

Hey guys I have year 10 yearlies soon and one of the topic is inverse function. However I am confused in regards to restricting a domain such that inverse f(x) exists. For example when y=x^3-3x is restricted and must include zero, the answer states the domain as -1<x<1 (which excludes the stationary points). However, an inverse sine function has a domain of -1≤x≤1, where the stationary point IS included. So how do I determine the domain?? Do I include or exclude the stationary points?

Are you saying that you've done calculus in year 10??

 

[pikachu975]

Lol yeah I'm from the top ruse class and I guess they learn in advance to other students . Btw It's not yearlies rather a topic test that could be in the yearlies but highly doubting it since no other class has done it lol

I don't think you learn inverse functions in year 10 it's part of 3U HSC though

 

[coyazayo]

I don't think you learn inverse functions in year 10 it's part of 3U HSC though

Lol I don't even understand what the teacher is saying ;p maybe I should talk to her about how its way past our syllabus huh?

 

[braintic]

I don't think you learn inverse functions in year 10 it's part of 3U HSC though

Stage 5.3 syllabus:

Determine the inverse functions for a variety of functions and recognise their graphs as reflections of the graphs of the functions in the line y=x

Describe conditions for a function to have an inverse function

Recognise and describe the restrictions that need to be placed on quadratic functions so that they have an inverse function