Definition of an inverse function problem

[priscilla98]

Homework Statement

Let f (x) have an inverse function g (x), then f(g(x)) =

A) 1
B) x
C) 1 / x
D) f (x) x g (x)
E) None of these


2. The attempt at a solution

I know the definition of an inverse function is Let f and g be two functions. If f(g(x)) = x and g(f(x)) = x, then g is the inverse of f and f is the inverse of g.

Functions f(x) and g(x) are inverses of one another if:

f(g(x)) = x and g(f(x)) = x,

for all values of x in their respective domains.


Therefore, could D be the answer?

 

[Dick]

If you say (correctly) that g is the inverse of f means f(g(x))=x then why would you answer D?

 

[priscilla98]

I guess I should have went with my first guess. I was thinking it couldn't be D. Okay then D is out, that can't be the answer. My second choice was C because I was looking that this answer is situated as a fraction

 

[Dick]

I guess I should have went with my first guess. I was thinking it couldn't be D. Okay then D is out, that can't be the answer. My second choice was C because I was looking that this answer is situated as a fraction

I don't know what's going through your head. You already said f(g(x))=x since g is the inverse of x. Doesn't that make the answer to the question 'what is f(g(x))' be 'x'. I.e. B? I'm not sure what is attracting you to the other answers. BTW saying 'g is an inverse of f' and 'g(x) is an inverse of f(x)' mean exactly the same thing. Is that what is throwing you?

 

[priscilla98]

By stating 'g is an inverse of f' and 'g(x) is an inverse of f(x)' mean exactly the same thing, is not confusing, i understand that part because g is still the inverse of f, it's just that your adding the x. The answer can't be B knowing that's the answer you would usually use when given values. Therefore, can the answer be B? Right, i understand this question, thanks a lot