# Thread: Rule of riciprocacy of inverse functions?

1. ## Rule of riciprocacy of inverse functions?

I'm in a debate with my math teacher over this, and she just doesn't understand what I'm asking. It's actually a pretty simple question. Is there a rule, law, or algebraic solution that states:

if $j(x)=h^-1(x)$ then $h(x)=j^-1(x)$

I was marked incorrectly on an assignment for refusing to make that assumption, and I refused to make that assumption because I was not able to find such a rule anywhere online or in the textbook. I don't mind being wrong if I actually am incorrect, I just want proof. Thanks in advance.

2. Originally Posted by ChrisEffinSmith
I'm in a debate with my math teacher over this, and she just doesn't understand what I'm asking. It's actually a pretty simple question. Is there a rule, law, or algebraic solution that states:

if $j(x)=h^-1(x)$ then $h(x)=j^-1(x)$

I was marked incorrectly on an assignment for refusing to make that assumption, and I refused to make that assumption because I was not able to find such a rule anywhere online or in the textbook. I don't mind being wrong if I actually am incorrect, I just want proof. Thanks in advance.

$j(x) = ln(x)$
$j^{-1}(x) = e^x$

$h(x) = e^x$
$h^{-1}(x) = ln(x)$

There may be a written rule for this somewhere, but it's actually mathematically true.