Question

Which function is equivalent to the inverse of y=sec(x)

Answer 1

From the identity:

$sec(x)= \frac{1}{cos(x)}$


$f(x)=sec(x)= \frac{1}{cos(x)}$

the inverse of f is g such that f(g(x))=x,

we must find g(x), such that $\frac{1}{cos[g(x)]}=x$

thus, $cos[g(x)]= \frac{1}{x}$

$g(x)=cos^{-1} (\frac{1}{x})$


Answer: b. g(x)=cos^-1(1/x)