Question

please help me with this
if f(x)=secx &g(x) is inverse of f(x) ,then when g(x) is derveted it become
g'(x)=1/|x|....,
why we insert x in absolute value

Answer 1

The inverse of \(\sec x=1/\sin x\) is \(g(x)=\sin^{-1}\frac{1}{x}\). The derivative of g does not contain a absolute value if we simplify it, in fact it is
\[ g'(x)=-\frac{1}{\sqrt{x^2-1}} \]