Question

How do I determine if these two equations are inverse?

Answer 1

compose them

Answer 2

t(x)= 4/x-1 and v(x)= x+4/x

Answer 3

compute
\[t(v(x))\]and see if you get \(x\)

Answer 4

I'm trying to figure out this first one. (t of v)(x)

Answer 5

\[t(x)=\frac{4}{x-1}, v(x)=\frac{x+4}{x}\] yes?

Answer 6

yes

Answer 7

\[t(v(x))=t(\frac{x+4}{x})\] is a start

Answer 8

then since
\[t(\clubsuit)=\frac{4}{\clubsuit-1}\] you have \[t(\frac{x+4}{x})=\frac{4}{\frac{x+4}{x}-1}\]

Answer 9

So far I have \[\frac{ 4 }{ (\frac{ x+4 }{ x })-1 }\]

I don't know how to continue from that.

Answer 10

multiply top and bottom by \(x\) to clear the compound fraction

Answer 11

gets your answer in basically one step

Answer 12

clear, or you want me to write it out?

Answer 13

Got it, thank you!

Answer 14

yw