Question

confirm that f and g are inverses by showing the f(g(x))=x and g(f(x))=x

f(x)=8/x and g(x)=8/x

Answer 1

hmm... what would f( g(x) ) look like?

Answer 2

\[y=\frac{ 8 }{ x }(\frac{ 8 }{ x })\]

Answer 3

@jdoe0001

Answer 4

\(\bf f(x)=\cfrac{8}{x}\qquad \color{red}{g(x)}=\cfrac{8}{x}\\ \quad \\
f(\quad g(x)\quad )=\cfrac{8}{\left(\color{red}{\frac{8}{x}}\right)}\)

Answer 5

how is it showing that it is an inverse though?

Answer 6

so let us simplify that..\(\bf f(\quad g(x)\quad )=\cfrac{8}{\left(\frac{8}{x}\right)}\implies \cfrac{\frac{8}{1}}{\left(\frac{8}{x}\right)}\\ \quad \\
\textit{recall that}\quad \cfrac{\quad \frac{a}{b}\quad }{\frac{c}{d}}\implies \cfrac{a}{b}\cdot \cfrac{d}{c}\qquad thus\\ \quad \\
\cfrac{\frac{8}{1}}{\frac{8}{x}}\implies
\cfrac{\cancel{8}}{1}\cdot \cfrac{x}{\cancel{8}}\)

Answer 7

so, indeed f( g(x) ) = x

so... try the g( f(x) ) , see what you'd get?