Additional Math

[Jezla]

Someone pls help me to find the range and domain of a function
Especially this question, May 2008 Paper 2 Question 11

 

[Zohaib Sherazi]

The question is given in completed square form. In this form (a+b)^2 + c . The range is always Y (is equal to and greater than) c. Which in this case is 2. The domain includes all the values that can be substituted for the variable x in the equation. So, alternatively you can work it out by substituting x =1 (given in the question as the least value of x for the equation) this gives y=2.

Similarly, if you are asked you to find the domain and range of the inverse of the same function then remember a straightforward shortcut: 'The inverse of a function is a reflection in the line y=x of the original function'. All you have to do is to reverse the domain and range values which we found earlier. So, the domain of the inverse of this function would become x (is equal to and greater than) 2. And its range will become y (is equal to and greater than 1).

If you have problem in any other part of this question then lemme knw.

 

[Jezla]

Allryt, then to find the range you have to only substitute xis greater or equal to -1? how about if one has to find the domain of the function (its not there in the question)???
And again to find the inverse don't we have to draw the graph?????? (that's wot my teacher taught me to find the range of the inverse)

 

[Zohaib Sherazi]

Ya.

 

[Zohaib Sherazi]

The question already states that take values of x(equal to and greater than) 1. And no, the graph is not at all a necessity. In examination conditions you won't even find that much time. In fact it will be a said waste of time. In this case the range can easily be calculated by using x (is equal to and greater than 1). Make a graph in your brain, the range is what the y-axis will have. It will be y(is equal to and greater than) 2. That will be lowest point on the y-axis. Beyond that it will go as much above as much as the values for x are stated, which in this case is anything equal to and greater than 1. Try making it for yourself to help yourself understand it

 

[Jezla]

domain??????

 

[Zohaib Sherazi]

The first part has its domain stated in the question. If there's any other part, then state it here. I'll go have a look.

 

[waleedbinqasim]

wat wud be the range of f(X)2sin^2x-1?????????