Restrict Domain of Function...2

[nycmathguy]

Section 1.9
Question 74

What does it mean to restrict
the domain of the function f so that the function is one-to-one and has an inverse function?

f(x) = (x - 4)^2

 

[MathLover1]

f(x) = (x - 4)^2 is a parabola

is not one-to-one, it will not pass horizontal test
to restrict the domain of the function f so that the function is one-to-one just go to vertex which is at x=4, and restrict domain to x<=4 to have only left half of the graph
or restrict domain to x>=4 to have only right half of the graph

 

[nycmathguy]

f(x) = (x - 4)^2 is a parabola

is not one-to-one, it will not pass horizontal test
to restrict the domain of the function f so that the function is one-to-one just go to vertex which is at x=4, and restrict domain to x<=4 to have only left half of the graph
or restrict domain to x>=4 to have only right half of the graph

In other words, cut or erase part of the graph so that it can pass the horizontal line test.

True?

 

[MathLover1]

True

 

[nycmathguy]

True

Just like that my weekend is over. I have a long week of work ahead. On 9/9/21, I move to my new place. I should have time for math at the new location as we continue our precalculus journey. I hope you can stick to the very end of the textbook. However, if you would like to shorten the journey, I can simply post midterm and final exam precalculus questions and then move into Calculus 1. The choice is yours. I would rather stay with the textbook.

 

[MathLover1]

just stay with the textbook

 

[nycmathguy]

just stay with the textbook

Ok. Will do. We move on to Section 1.10 or Mathematical Modeling in terms of variation problems.