The function f(x)=(x+7)^2 is not one-to-one. Choose a largest possible domain containing the number 100 so that the function restricted to the domain is one-to-one.

Question

zale101 · Answer

if a function is one-to-one that means every y-value corresponds to only one x-value

ranga · Answer

This is a parabola with vertex at (-7,0).
The graph will be symmetrical about the vertical line x = -7
If the function is restricted to the right of x = -7 or to the left of x = -7 it will be a one-to-one function.  They tell you to include 100 in the domain.  Therefore you have to choose the domain to the right of x = -7 (including x = -7).

So the domain will be ?

ranga · Answer

In the domain {-7, infinity) the function will be one-to-one.  Each y-value will have a unique x-value.

anonymous · Answer

thank you! i got confused with the 100 thrown in there.

ranga · Answer

You are welcome.

Yeah, there is a bit of ambiguity in the question.  If they are saying the largest possible number in the domain is 100 then the domain will be [-7, 100].  But if they are saying the largest possible domain that includes the number 100 then it will be [-7, infinity).

I just noticed the typo above.  The bracket should not be curly bracket '{' but a square bracket '['.   The domain is  [-7, infinity).