Let f be a 1-1 function such that f(a) = b, f(b) = c, and f(c) = a. Find the following.
f −1(f −1(c))

Question

anonymous · Answer

deja vu

anonymous · Answer

i tryied asking you to explain more 
tryign to get it

anonymous · Answer

oh ok we take it one step at at time

anonymous · Answer

thank you

anonymous · Answer

we know 
$$f(a)=b$$ so we also know that 
$$f^{-1}(b)=a$$ so far ok?

anonymous · Answer

yes

anonymous · Answer

also we have 
$$f(b)=c$$ so we know 
$$f^{-1}(c)=b$$ right?

anonymous · Answer

yes

anonymous · Answer

so what does 
$$f^{-1}(f^{-1}(c))$$ mean? it means first find 
$$f^{-1}(c)$$ and then find 
$$f^{-1}$$ of the result

anonymous · Answer

so writing it out we get 
$$f^{-1}(f^{-1}(c))=f^{-1}(b)$$ and that is true because we know 
$$f^{-1}(c)=b$$

anonymous · Answer

next step is 
$$f^{-1}(b)=a$$ which we also knew from above

anonymous · Answer

writing this in one line we get 
$$f^{-1}(f^{-1}(c))=f^{-1}(b)=a$$ and that is what you wanted

anonymous · Answer

make sense or still confusing?

anonymous · Answer

okay i am getting it..so the answer is simple a or do i write if F-1(b)+a

anonymous · Answer

no answer is simply "a"

anonymous · Answer

there is no "+" involved

anonymous · Answer

meant = sorry

anonymous · Answer

sweet thank you i am pretty sure  i get it now

anonymous · Answer

oh ok, the answer is just "a"

anonymous · Answer

for example if you know 
$$2x-1=7$$ then you know that 
$$x=4$$ this is like saying 
$$f(x)=2x-1$$ and 
$$f(4)=7$$ 
$$f^{-1}(7)=4$$

anonymous · Answer

okay cool thank you

anonymous · Answer

yw