Question

Assume that the function f is a one-to-one function.
If (f(1) = 4, find (f(1))^-1

Answer 1

I think the answer is just the inverse of 4 which is 1/4. How would I show steps for this kind of problem?

Answer 2

I don't think so, but I don't know how to solve since it is not enough information to solve

Answer 3

That is all the information that I have from the textbook

Answer 4

inverse of f(1) are you sure?

Answer 5

yes, inverse of f(1)

Answer 6

I am sorry, above my head.

Answer 7

inverse function is denoted as f^-1(x).
Note that this isn't the same as [f(x)]^-1 = 1/f(x).

As for the question, all we can conclude is (4,1) is an element of f^-1.
There is not enough information to evaluate f^-1(1)

Answer 8

Are you sure it is not 1/4? We are given that f(1) = 4 so f(1)) - 1 would say the inverse of 4... that is the way I am approaching it.

Answer 9

wrong way!! get ticket

Answer 10

I think you got the terminology confused. Inverse isn't the same as flipping a fraction.

Answer 11

I worked out a similar problem which is if f(5) = 2, find (f(5))^-1 and the answer was 1/2 so I concluded that they got that answer by taking the inverse of the x value

Answer 12

This one was given in the back of the book

Answer 13

If that is the case, the correct terminology is *reciprocal*

Answer 14

that is what I would call it... but the book insists on using the word "inverse" for this whole section

Answer 15

from the textbook: if (f(a) = b, then a function g(x) is an inverse of f if g(b) = a

Answer 16

the inverse is typically nottated f^-1(x), which is read "f inverse of x", so if f(a) = b then f ^ -1(b) = a

Answer 17

but to me that means reciprocal of a function

Answer 18

ok, then this isn't the same as [1/f(x)] like I mentioned earlier

Answer 19

going by their definition, my answer would be correct?

Answer 20

no, 1/4 isn't the answer.

read the definition carefully again. It says
given f(a) = b. If g is the inverse of f, then g(b) = a.

so, given f(1) = 4. we known f^-1 is the inverse of f, then f^-1(4) = 1. This much we know. There isn't enough info to evaluate f^-1(1)

Answer 21

so we can only evaluate what we know

Answer 22

yes, i would put "not enough info" as the answer to this question

Answer 23

The original problem does not say anything about inverse function. As it is written (reciprocal of a function value) the solution should be 1/4. If this problem shows up along with the definition of inverse functions, then this might possibly be a gotcha exercise to teach you to distinguish between f^{-1}(.) and (f(.))^{-1} as these get confused.

Answer 24

so does (f(1))^-1 mean reciprocal and not inverse function?

Answer 25

@b87lar

Answer 26

Would you show any steps for this problem? I was just going to write it as