Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f(x) = 8/x and g(x)=8/x
i don't get what to do when you have 8/8/x ???
some one please help

Answer 1

\[f \left( g \left( x \right) \right)=\frac{ 8 }{ g \left( x \right) }\]
put in g(x)

hint:
\[\frac{ \frac{ a }{ b } }{ \frac{ c }{ d } }=\frac{ a }{ b }\times \frac{ d}{ c }\]

Answer 2

think of numerator, 8, as
\[\frac{ 8 }{ 1 }\]

Answer 3

ohh right if youre dividing you can multiply by its inverse! thank you

Answer 4

very good and you're welcome!

Answer 5

wait

Answer 6

then what do i do with 8/1 x x/8??

Answer 7

\[\frac{ 8 }{ 1 }\times \frac{ x }{ 8 }=\frac{ 8x }{ 8 }=?\]

Answer 8

and so, that is the same answer for both and that proves that they are inverses?

Answer 9

yes. they're inverses, they take you back to where you started.
f(x) = g(x) = 8/x, right. so let's say you want to find f(g(3)). that says to plug in the y that you get when you plug in 3 for x in g(x).
that y is 8/3 and now you plug that in for x in f(x) and you get
8/(8/3) = (8/1) x (3/8) = 3
that's the original x you started with. it took you back.

Answer 10

thankiyiou

Answer 11

you're welcome

Answer 12

do you know the graph of 1/x?
it's symmetric about the line y = x which is why it is its own inverse.

Same for y = k/x where k is any non-zero constant