how to find inverse image of function

[Semidevil]

ok, so given f(x) = 1/x^2, I need to determine the idrect image f(E) where E := { 1<= x <= 2 }. ok, so for direct image, I just plug in, and the answer is {1 <= x <= 1/4}.

what is the inverse image inverse image where G:= { 1 <= x <= 4}.

I'm just flat out not understanding how to find an inverse image of anyhing.......can someone give me some tips? what do I do with the given numbers?

edit: so basically, are they saying that the direct image is {1 <= x <=4}, and I need to work backwards?

if so, im just guessing, buy maybe {-1/2 <= x <= 1/2}?

 

[chuckywang]

Originally posted by: Semidevil
ok, so given f(x) = 1/x^2, I need to determine the idrect image f(E) where E := { 1<= x <= 2 }. ok, so for direct image, I just plug in, and the answer is {1 <= x <= 1/4}.

Actually 1<=f(x)<=1/4

what is the inverse image inverse image where G:= { 1 <= x <= 4}.

Once again, I think you mean to say 1<=f(x)<=4, so what values of x make f(x) in this interval?
You'll see it's when 1/2<=x<=1 and -1<=x<=-1/2.

I'm just flat out not understanding how to find an inverse image of anyhing.......can someone give me some tips? what do I do with the given numbers?

edit: so basically, are they saying that the direct image is {1 <= x <=4}, and I need to work backwards?

if so, im just guessing, buy maybe {-1/2 <= x <= 1/2}?