Question

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

Answer 1

\[f(x) = \frac{ 4}{ x } \]
and \[g(x)= \frac{ 4 }{ x }\]

Answer 2

\[\large\rm f(\color{orangered}{x})=\frac{4}{\color{orangered}{x}}\]Ok let's try one of the directions,
let's plug g into our f,\[\large\rm f(\color{orangered}{g(x)})=\frac{4}{\color{orangered}{g(x)}}\]Replacing g(x) with 4/x in our function gives us,\[\large\rm f(\color{orangered}{g(x)})=\frac{4}{\color{orangered}{\frac4x}}\]

Answer 3

Remember what to do when dividing by a fraction?
Have you learned `Keep Change Flip` or something similar perhaps?

Answer 4

yeah

Answer 5

@zepdrix

Answer 6

\(\large\rm \dfrac{a}{\frac{b}{c}}=a\cdot\frac{c}{b}\)

`Keep` the numerator the same,
`Change` the operation from division to multiplication,
`Flip` the bottom fraction.

Answer 7

so it would be \[4 \times \frac{ x }{ 4 }\]

Answer 8

Yes, and then deal with the 4's :)
Cancellation, yes?

Answer 9

yes so \[1\times x\]

Answer 10

@zepdrix

Answer 11

Ya so it looks like f(g(x)) = x
Good.

Answer 12

thank you @zepdrix

Answer 13

Can you try the other direction on your own? :)
It should be very similar.

Answer 14

Oh, actually, it's exactly the same lol