Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f of x equals four divided by x. and g of x equals four divided by x

Answer 1

@triciaal

Answer 2

@jim_thompson5910 this is a writing portion

Answer 3

\[f(x)=\frac{4}{x}\] right?

Answer 4

yes

Answer 5

and also \(g(x)=\frac{4}{x}\)

Answer 6

yes

Answer 7

so what you need is to compute \[f(g(x))\] which only takes two steps
first \[f(g(x))=f(\frac{4}{x})\]

Answer 8

then since \[f(\heartsuit)=\frac{4}{\heartsuit}\] you get \[\large f(\frac{4}{x})=\frac{4}{\frac{4}{x}}\]

Answer 9

a little algebra will turn \[\frac{4}{\frac{4}{x}}\] in to \(x\), which is what you want

Answer 10

what are the hearts for?

Answer 11

place holders so you can understand why \[\large f(\frac{4}{x})=\frac{4}{\frac{4}{x}}\]

Answer 12

ohh okay :) thank you! Do I put everything you told me from your 3rd message to your 5th message?

Answer 13

yes, i think so

Answer 14

the point is that \[\large f(g(x))=f(\frac{4}{x})=\frac{4}{\frac{4}{x}}=4\times \frac{x}{4}=x\] and since \(f(g(x))=x\) that means they are inverses
or rather "the function is its own inverse"