Expert: Socrates - 5/15/2007

Question
hi i am trying to complete this question. the diagram is one of a graph of the function f(x)=(x^2)+1,-1<=x<=1 and p,q E(element) R.(i)find value of p & q.[coordinates are at (-1,p) & (q,2). Ans-: I found p to be '2' and q to be '1' by subbing directly into the function (ii)the range of the function f(x) for the given domain Ans-: -1<=x<=1 (I got this range directly from the given info; is there a way to show working?)(b(i)) Determine whether f(x) is surjective(onto) (ii)is injective (one-to-one) (iii) has an inverse.
Now, I am not sure how to do these last ones. could you please help me. thank you in advance for you help

Answer
i)
p=2 and q = 1 OR q = -1 ( either value for q will work )

ii)
the range of this function is  1 =< f(x) <= 2, (the smallest value for the function occurs when x=0 , the largest when x is 1 or x is -1 , to see this , just look at the graph)

The function is surjective onto [1 , 2] , again , just look at the graph. You see that the "y" coordinates for points on the graph can be any number between 1 and 2

The function is not injective , two different values for x  can give the same function value.
For example f(1) = f(-1) = 2

The function has no inverse. To have an inverse , a function must be injective and surjective . This function is not injective.