Question

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

Answer 1

plug in f(g(x)) and simplify

Answer 2

recall that division = multiplication by the reciprocal

Answer 3

i'm so lost and confused right now.. could you please show it?

Answer 4

what does \(f(g(x))\) mean?

it means we're pluggin in what g(x) is as f(x)'s input
\(f(g(x))=f(\dfrac{2}{x})\)

Answer 5

Oh okay, but like how do i confirm it? What does it all mean? Like i have no clue what I'm suppose to be putting in that box

Answer 6

\[\Large \color{blue}{g(x) = \frac{2}{x}}\]
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\[\Large f(x) = \frac{2}{x}\]
\[\Large f(\color{blue}{g(x)}) = \frac{2}{\color{blue}{g(x)}}\]
\[\Large f(\color{blue}{g(x)}) = \frac{2}{\color{blue}{2/x}}\]
\[\Large f(g(x)) = \frac{2/1}{2/x}\]
\[\Large f(g(x)) = \frac{2}{1}*\frac{x}{2}\]
I'll let you simplify
You'll need to do similar steps for `g(f(x))`