inverse functions?

Question

if f is one-to-one f(3)=7
then f^-1(7)=3

and (f(3))^-1 is ?????????

Answer 1

(f(3))^-1 = 1 / f(3) = 1 / 7

I agree that since f is 1-1, then f^-1(x) is the inverse function of f(x) and (f^-1)^-1(x) is the inverse function of the inverse function of f(x), i.e. it is just f(x) again.
However, (f(x))^-1 denotes the inverse of the value of f(x) and so it is 1 / f(x).

Answer 2

To keep from being confused draw two circles with arrows pointing from each circle to the other circle.

Label arrows going from circle A to circle B as f, and arrows going from circle B to A as f inverse.

f(3) = 7 therefore f_inverse(f(3)) = f_inverse(7) = 3

There can be some confusion as to notation between the recipicol of f and the inverse. On Answers usually the ^-k notation means the power function to the power of -k

Answer 3

Assuming you mean f(f(3))^-1, the answer would be 3.
Since f(3) = 7, then you can simplify the question to be:
f(7)^-1, which from the definition is 3.

Answer 4

Your question doesn't seem to make sense to me. Please clarify and use correct notation.

PS - from the information present, f^-1(x) does not necesarily equal 1/f(x)