Question

Please check my answer and help me with b)

Answer 1

For A i got f^-1(x)+2(x-1)

Answer 2

oops before the 2 it's a = not a +

Answer 3

f^-1(x) = 2(x-1)

Answer 4

Is that correct? How do I do b?
I have been searching everywhere and every explanation confuses me even more.

Answer 5

@Elsa213

Answer 6

@morganchavez

Answer 7

@HeatDude

Answer 8

@haleyelizabeth2017

Answer 9

I think....so..........? I have no idea. I'm sorry! I didn't have to learn this last year so yeah.......:/

Answer 10

Could you please tag someone who you think could help me?

Answer 11

@micahm

Answer 12

post question

Answer 13

Huh?

Answer 14

The q is attached as a photo

Answer 15

go to this site and this will tell you if your right
http://www.freemathhelp.com/

Answer 16

✔

Answer 17

mmmm.... the question is in a photo and I was just wondering if anyone could help me solve it.

Answer 18

That website isn't much help :/

Answer 19

http://www.wolframalpha.com/input/?i=f(x)%3d1%2f2x%2b1+inverse

Answer 20

i did it go there

Answer 21

and if u wanna make double sure of ur answer go to mathway.com it wont give u steps but it will tell u the right answer

Answer 22

wait, how will it tell me the right answer?

Answer 23

by the way, my problem says it has to have steps of how I got there... so how do I do THAT now.

Answer 24

a is correct.

Answer 25

As for b, function composition means that you 'insert' a function in another function to produce a third one.

So for example
f(x) = x + 2
g(x) = x - 3
have at least one composite function c(x)
c(x) = f(g(x)) = g(x) + 2 = (x - 3) + 2 = x - 1

In your case we know that the inverse of a function is infact the same as expressing the functon in terms of f(x) instead of x.
\[f(x) = \frac{ 1 }{ 2 } x + 1 \rightarrow x = 2 (f(x) - 1)\]
You know that the right side is equal to the inverse, but instead of re-writing it as a relation of x to f^-1(x) you keep it as a relation of f(x) to f^-1(f(x)).
\[f^{-1}(f(x)) = 2(f(x)-1)\]
From this you get that the function composition\[f^{-1}(f(x)) = x\]
This means that all you have to do in b is to insert the function as a value in the inverse function and show that the answer is equal to x.

Something like this
\[f^{-1}(f(x)) = 2((\frac{ 1 }{ 2 } x -1) + 1) = x\]which is what we predicted.

@ilovchuu