Question

for the function 14/x+3, find (g^-1og)(4). I came up with the inverse y=14-3x/x. (not sure if that is right) and then I thought I had to sub. 4 in for x but that doesn't work. Choices for answers are : 6, 10, 4 or 0.

Answer 1

Is this the given function?\[g(x)=\frac{ 14 }{ x+3 }\]

Answer 2

yes, it is a fraction

Answer 3

If so\[g^{-1}(x)=\frac{ 14-3x }{ x }\]Thus
\[(g^{-1}og)(x)=g^{-1}(g(x))=\frac{ 14-3(g(x)) }{ g(x) }\]
\[(g^{-1}og)(x)=g^{-1}(g(x))=\frac{ 14-3(g(x)) }{ g(x) }\]
\[(g^{-1}og)(4)=g^{-1}(g(4))=\frac{ 14-3(g(4)) }{ g(4) }\]
which is 4

Answer 4

I don't quite see what is happening. What is the inverserse? Once you found the inverse did you sub. 4 for x or is the answer 4 becs. that was what was given to us in question?

Answer 5

is this what you are saying? 4=14-3(4)=4?

Answer 6

There is a postulate if you want know either, it says
\[(f^{-1}of)(x)=x\]

Answer 7

Did you get it?

Answer 8

no

Answer 9

did I get the inverse correct

Answer 10

yep

Answer 11

ok, after finding the inverse do I sub 4 in for x?

Answer 12

No sub g(x) in the place of x of the inverse function

Answer 13

ok what is g(x)? what is done with the 4 that is given

Answer 14

is g(x) the orginial equation?

Answer 15

I mean g(4)

Answer 16

yep

Answer 17

so I need to solve for this equation to get my answer ? y={14-3(14/x+3)}/14/x+3 what happens to the 4 in the given question?

Answer 18

yes, then insert 4 in place x here.

Answer 19

oh--okay I get it. Thanks

Answer 20

so what was thee Answer? please...

Answer 21

so the right answer is 4